]>
2015
8
3
ISSN 2008-1898
110
Lower and upper solutions for a discrete first-order nonlocal problems at resonance
Lower and upper solutions for a discrete first-order nonlocal problems at resonance
en
en
We discuss the existence of solutions for the discrete first-order nonlocal problem
\[
\begin{cases}
\Delta u(t - 1) = f(t, u(t)),\quad t \in \{1, 2, ... , T\},\\
u(0) +\Sigma_{i=1}^m \alpha_iu(\xi_i) = 0,
\end{cases}
\]
where \(f : \{1,..., T\} \times \mathbb{R}\rightarrow \mathbb{R}\) is continuous, \(T > 1\) is a fixed natural number, \(\alpha_i \in (-\infty; 0],\, \xi_i \in \{1,...,T\}(i = 1,..., m; 1 \leq m \leq T; m \in \mathbb{N})\) are given constants such that
\(\Sigma_{i=1}^m \alpha_i+ 1 = 0\). We develop the
methods of lower and upper solutions by the connectivity properties of the solution set of parameterized
families of compact vector fields.
174
183
Faxing
Wang
TongDa College of Nanjing University of Posts and Telecommunications
China
wangfx@njupt.edu.cn
Ying
Zheng
College of Science
Nanjing University of Posts and Telecommunications
China
zhengying@njupt.edu.cn
Coincidence point
first-order discrete nonlocal problem
contraction
lower and upper solutions
connected sets.
Article.1.pdf
[
[1]
R. D. Anderson, Existence of three solutions for a first-order problem with nonlinear nonlocal boundary conditions, J. Math. Anal. Appl., 408 (2013), 318-323
##[2]
D. Y. Bai, Y. T. Xu, Nontrivial solutions of boundary value problems of second-order difference equations, J. Math. Anal. Appl., 326 (2007), 297-302
##[3]
E. Carlini, F. J. A. Silva , Fully Discrete Semi-Lagrangian Scheme for a First Order Mean Field Game Problem Carlinilly Discrete Semi-Lagrangian Scheme for a First Order Mean Field Game Problem, J. Numerical Anal., 52 (2014), 45-47
##[4]
S. C. Goodrich, On a first-order semipositone discrete fractional boundary value problem, Arch. Math. (Basel), 99 (2012), 509-518
##[5]
J. Henderson, Positive solutions for nonlinear difference equations, Nonlinear Stud., 4 (1997), 29-36
##[6]
J. Henderson, H. B. Hompson, Thompson. Existence of multiple solutions for second-order discrete boundary value problems, Comput. Math. Appl., 43 (2002), 1239-1248
##[7]
J. Mawhin, P. M. Fitzpatric, Topological degree and boundary value problem for nonlinear differential equations, Lecture Notes in Math., 1537 (1991), 74-172
##[8]
L. Nizhnik, Inverse spectral nonlocal problem for the first order ordinary differential equation, Archiv. der. Mathematik, 99 (2012), 509-518
##[9]
R. Y. Ma, Multiplicity results for a three-point boundary value problem at resonance, Nonlinear Anal., 53 (2003), 777-789
##[10]
R. Y. Ma, Existence and uniqueness of solutions to first-order three-point boundary value problems, Appl. Math. Letters, 15 (2002), 211-216
##[11]
R. Y. Ma, Multiplicity results for an m-point boundary value problem at resonance, Indian J. Math., 47 (2005), 15-31
##[12]
E. Mahmudov, Optimal control of Cauchy problem for first-order discrete and partial differential inclusions, J. Dyn. Control Syst., 15 (2009), 587-610
##[13]
H. H. Pang, H. Y. Feng, W. G. Ge, Multiple positive solutions of quasi-linear boundary value problems for finite difference equations , Appl. Math. Comput., 197 (2008), 451-456
##[14]
P. J. Y. Wong, R. P. Agarwal , Fixed-sign solutions of a system of higher order difference equations , J. Comput. Appl. Math., 113 (2000), 167-181
##[15]
R. P. Agarwal, D. O'Regan , Nontrivial solutions of boundary value problems of second-order difference equations, Nonlinear Anal., 39 (2000), 207-215
##[16]
J. P. Sun, Positive solution for first-order discrete periodic boundary value problem, Appl. Math. Letters, 19 (2006), 1244-1248
##[17]
J. P. Sun, W. T. Li , Existence of positive solutions of boundary value problem for a discrete difference system, Appl. Math. Comput., 156 (2004), 857-870
##[18]
P. X. Weng, Z. H. Guo, Existence of Positive Solutions for BVP of Nonlinear Functional Difference Equation with p-Laplacian Operator, Acta Math. Sinica, 1 (2006), 187-194
]
A coincident point and common fixed point theorem for weakly compatible mappings in partial metric spaces
A coincident point and common fixed point theorem for weakly compatible mappings in partial metric spaces
en
en
In this paper, we prove the existence of a coincident point and a common fixed point for two self mappings
defined on a complete partial metric space \(X\). We will consider generalized cyclic representation of the set \(X\)
with respect to the two self maps defined on \(X\) and a contractive condition involving a generalized distance
altering function. Our results generalizes several corresponding results in the existing literature.
184
192
M.
Akram
Department of Mathematics and Statistics, College of Science
King Faisal University
Kingdom of Saudi Arabia
maahmed@kfu.edu.sa;dr.makram@gcu.edu.pk
W.
Shamaila
Department of Mathematics
Kinnaird College for Women
Pakistan
shamailawaheed20@gmail.com
Coincidence point
fixed point
contraction
partial metric space.
Article.2.pdf
[
[1]
M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416-420
##[2]
T. Abdeljawad, J. O. Alzabut, A. Mukheimer, Y. Zaidan, Banach contraction principle for cyclical mappings on partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-7
##[3]
R. P. Agarwal, M. A. Alghamdi, N. Shahzad, Fixed point theory for cyclic generalized contractions in partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-11
##[4]
I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-10
##[5]
H. Aydi, E. Karapinar, A fixed point result for Boyd-Wong cyclic contractions in partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-11
##[6]
H. Aydi, C. Vetro, W. Sintunavarat, P. Kumam, Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-18
##[7]
S. Banach, Sur certains ensembles de fonctions conduisant aux quations partielles du second ordre , (French) Math. Z., 27 (1928), 68-75
##[8]
C. Di Bari, C. Vetro , Common fixed point theorems for weakly compatible maps satisfying a general contractive condition, Int. J. Math. Math. Sci., 2008 (2008), 1-8
##[9]
S. Chandok, M. Postolache, Fixed point theorem for weakly Chatterjea-type cyclic contractions, Fixed Point Theory Appl., 2013 (2013), 1-9
##[10]
C. M. Chen , Fixed point theory of cyclical generalized contractive conditions in partial metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-15
##[11]
B. S. Choudhury, A common unique fixed point result in metric spaces involving generalised altering distances, Math. Commun., 10 (2005), 105-110
##[12]
B. S. Choudhury, P. N. Dutta, A unified fixed point result in metric spaces involving a two variable function, Filomat, 14 (2000), 43-48
##[13]
R. Heckmann, Approximation of metric spaces by partial metric spaces, Applications of ordered sets in computer science (Braunschweig, 1996), Appl. Categ. Structures, 7 (1999), 71-83
##[14]
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771-779
##[15]
E. Karapinar, I. M. Erhan, A. Y. Ulus, Fixed point theorem for cyclic maps on partial metric spaces , Appl. Math. Inf. Sci., 6 (2012), 239-244
##[16]
E. Karapinar, H. K. Nashine, Fixed point theorems for Kannan type cyclic weakly contractions, J. Nonlinear Anal. Optim., 4 (2013), 29-35
##[17]
E. Karapinar, K. Sadarangani, Fixed point theory for cyclic (\(\phi-\psi\) )-contractions, Fixed Point Theory Appl., 2011 (2011), 1-8
##[18]
E. Karapinar, N. Shobkolaei, S. Sedghi, S. M. Vaezpour, A common fixed point theorem for cyclic operators on partial metric spaces, Filomat, 26 (2012), 407-414
##[19]
M. S. Khan, M. Swaleh,S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1-9
##[20]
W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), 79-89
##[21]
H.-P. A. Knzi, H. Pajoohesh, M. P. Schellekens, Partial quasi-metrics, Theoret. Comput. Sci., 365 (2006), 237-246
##[22]
S. G. Matthews, Partial metric topology. , Research Report 212. Dept. of Computer Science, University of Warwick (1992)
##[23]
S. G. Matthews, Partial metric topology , Papers on general topology and applications (Flushing, NY, 1992), 183-197, Ann. New York Acad. Sci., 728, New York Acad. Sci., New York (1994)
##[24]
M. Bukatin, R. Kopperman, S. Matthews, H. Pajoohesh, Partial metric spaces, Amer. Math. Monthly, 116 (2009), 708-718
##[25]
D. Mihet , Altering distances in probabilistic Menger spaces, Nonlinear Anal., 71 (2009), 2734-2738
##[26]
S. V. R. Naidu, Some fixed point theorems in metric spaces by altering distances, Czechoslovak Math. J., 53 (2003), 205-212
##[27]
S. J. O'Neill, Partial metrics, valuations, and domain theory, Papers on general topology and applications (Gorham, ME, 1995), Ann. New York Acad. Sci., New York Acad. Sci., New York, 860 (1996), 304-315
##[28]
M. Pacurar, I. A. Rus, Fixed point theory for cyclic \(\phi\)-contractions, Nonlinear Anal., 72 (2010), 1181-1187
##[29]
M. A. Petric, Some results concerning cyclical contractive mappings, Gen. Math., 18 (2010), 213-226
##[30]
S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl., 2010 (2010), 1-6
##[31]
S. Romaguera, M. Schellekens, Duality and quasi-normability for complexity spaces, Appl. Gen. Topol., 3 (2002), 91-112
##[32]
S. Romaguera, M. Schellekens, Partial metric monoids and semivaluation spaces, Topology Appl., 153 (2005), 948-962
##[33]
S. Romaguera, O Valero, A quantitative computational model for complete partial metric spaces via formal balls, Math. Structures Comput. Sci., 19 (2009), 541-563
##[34]
I. A. Rus, Cyclic representations and fixed point, Ann T. Popviciu seminar funct. Eq. Approx. convexity, 3 (2005), 171-178
##[35]
K. P. R. Sastry, G. V. R. Babu, Some fixed point theorems by altering distances between the points, Indian J. Pure Appl. Math., 30 (1999), 641-647
##[36]
M. P. Schellekens, A characterization of partial metrizability: domains are quantifiable, Topology in computer science (Schloss Dagstuhl, 2000), Theoret. Comput. Sci., 305 (2003), 409-432
]
Positive solutions for a second-order delay p--Laplacian boundary value problem
Positive solutions for a second-order delay p--Laplacian boundary value problem
en
en
This paper investigates the existence and multiplicity of positive solutions for a second-order delay p-
Laplacian boundary value problem. By using fixed point index theory, some new existence results are
established.
193
200
Keyu
Zhang
Department of Mathematics
Qilu Normal University
China
keyu_292@163.com
Jiafa
Xu
School of Mathematics
Chongqing Normal University
China
xujiafa292@sina.com
p-Laplacian equation
delay
positive solution
fixed point index.
Article.3.pdf
[
[1]
R. Agarwal, Ch. Philos, P. Tsamatos , Global solutions of a singular initial value problem to second order nonlinear delay differential equations, Math. Comput. Modelling, 43 (2006), 854-869
##[2]
C. Bai, J. Ma, Eigenvalue criteria for existence of multiple positive solutions to boundary value problems of second-order delay differential equations, J. Math. Anal. Appl., 301 (2005), 457-476
##[3]
D. Bai, Y. Xu, Positive solutions and eigenvalue intervals of nonlocal boundary value problems with delays, J. Math. Anal. Appl., 334 (2007), 1152-1166
##[4]
D. Bai, Y. Xu, Positive solutions of second-order two-delay differential systems with twin-parameter, Nonlinear Anal., 63 (2005), 601-617
##[5]
D. Bai, Y. Xu, Positive solutions and eigenvalue regions of two-delay singular systems with a twin parameter, Nonlinear Anal., 66 (2007), 2547-2564
##[6]
B. Du, X. Hu, W. Ge, Positive solutions to a type of multi-point boundary value problem with delay and one- dimensional p-Laplacian, Appl. Math. Comput., 208 (2009), 501-510
##[7]
C. Guo, Z. Guo, Existence of multiple periodic solutions for a class of second-order delay differential equations, Nonlinear Anal. Real World Appl., 10 (2009), 3285-3297
##[8]
D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Orlando (1988)
##[9]
C. Jin, J. Yin , Positive solutions for the boundary value problems of one-dimensional p-Laplacian with delay, J. Math. Anal. Appl., 330 (2007), 1238-1248
##[10]
D. Jiang, X. Xu, D. O'Regan, R. Agarwal , Existence theory for single and multiple solutions to singular positone boundary value problems for the delay one-dimensional p-Laplacian, Ann. Polon. Math., 81 (2003), 237-259
##[11]
H. Walther, Differential equations with locally bounded delay, J. Differential Equations, 252 (2012), 3001-3039
##[12]
K. Wu, X. Wu, F. Zhou, Multiplicity results of periodic solutions for a class of second order delay differential systems, Nonlinear Anal., 75 (2012), 5836-5844
##[13]
Y. Wang, W. Zhao, W. Ge, Multiple positive solutions for boundary value problems of second order delay differential equations with one-dimensional p-Laplacian, J. Math. Anal. Appl., 326 (2007), 641-654
##[14]
Y. Wei, P. J. Y. Wong, W. Ge, The existence of multiple positive solutions to boundary value problems of nonlinear delay differential equations with countably many singularities on infinite interval , J. Comput. Appl. Math., 233 (2010), 2189-2199
##[15]
J. Xu, Z. Yang, Positive solutions for a fourth order p-Laplacian boundary value problem, Nonlinear Anal., 74 (2011), 2612-2623
]
Some inequalities of Hermite-Hadamard type for n--times differentiable (\(\rho, m\))--geometrically convex functions
Some inequalities of Hermite-Hadamard type for n--times differentiable (\(\rho, m\))--geometrically convex functions
en
en
In this paper, some generalized Hermite-Hadamard type inequalities for n-times differentiable (\(\rho, m\))-
geometrically convex function are established. The new inequalities recapture and give new estimates of
the previous inequalities for first differentiable functions as special cases. The estimates for trapezoid, midpoint,
averaged mid-point trapezoid and Simpson's inequalities can also be obtained for higher differentiable
generalized geometrically convex functions.
201
217
Fiza
Zafar
Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM)
Bahauddin Zakariya University
Pakistan
fizazafar@gmail.com
Humaira
Kalsoom
Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM)
Bahauddin Zakariya University
Pakistan
humaira.k86@gmail.com
Nawab
Hussain
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nhusain@kau.edu.sa
Hermite-Hadamard inequality
(\(\rho، m\))-geometrically convex functions
n-times differentiable function.
Article.4.pdf
[
[1]
P. Cerone, S. S. Dragomir, Three point identities and inequalities for n-time differentiable functions, SUT. J., 36 (2000), 351-384
##[2]
S. S. Dragomir, Two mappings in connection to Hadamard's inequality, J. Math. Anal. Appl., 167 (1992), 49-56
##[3]
S. S . Dragomir, R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91-95
##[4]
S. S. Dragomir, J. E. Pečarić, J. Sándor, A note on the Jensen-Hadamard's inequality, Anal. Num. Ther. Approx., 19 (1990), 29-34
##[5]
M. Masjed-Jamei, N. Hussain, More results on a functional generalization of the Cauchy-Schwarz inequality, J. Inequal. Appl., 2012 (2012), 1-9
##[6]
P. Montel , Sur les functions convexes et les fonctions sousharmoniques, J. Math. Inequal., 9 (1928), 29-60
##[7]
M. E. Özdemir, C. Yildiz, New Ostrowski type inequalities for geometrically convex functions, Int. J. Mod. Math. Sci., 8 (2013), 27-35
##[8]
Bo-Yan Xi, Rui-Fang Bai, Feng Qi , Hermite-Hadamard type inequalities for the m-and (\(\alpha,m\))-geometrically convex functions, Aequationes Math., 84 (2012), 261-269
##[9]
X. M. Zhang , Geometrically Convex Functions, Anhui University Press(In Chinese). , Hefei (2004)
##[10]
X. M. Zhang, Y. M. Chu, The geometrical convexity and concavity of integral for convex and concave functions, Int. J. Mod. Math., 3 (2008), 345-350
##[11]
X. M. Zhang, Z. H. Yang, Differential criterion of n-dimensional geometrically convex functions, J. Appl. Anal., 13 (2007), 197-208
##[12]
X. M. Zhang, An inequality of the Hadamard type for the geometrically convex functions (in Chinese), Math. Pract. Theory, 34 (2004), 171-176
]
Approximate ternary quadratic derivation on ternary Banach algebras and \(C^*\)-ternary rings revisited
Approximate ternary quadratic derivation on ternary Banach algebras and \(C^*\)-ternary rings revisited
en
en
Recently, Shagholi et al. [S. Shagholi, M. Eshaghi Gordji, M. B. Savadkouhi, J. Comput. Anal. Appl.,
13 (2011), 1097-1105] defined ternary quadratic derivations on ternary Banach algebras and proved the
Hyers-Ulam stability of ternary quadratic derivations on ternary Banach algebras. But the definition was
not well-defined.
Using the fixed point method, Bodaghi and Alias [A. Bodaghi, I. A. Alias, Adv. Difference Equ., 2012
(2012), 9 pages] proved the Hyers-Ulam stability and the superstability of ternary quadratic derivations
on ternary Banach algebras and \(C^*\)-ternary rings. There are approximate \(\mathbb{C}\)-quadraticity conditions in the
statements of the theorems and the corollaries, but the proofs for the \(\mathbb{C}\)-quadraticity were not completed. In
this paper, we correct the definition of ternary quadratic derivation and complete the proofs of the theorems
and the corollaries.
218
223
Choonkill
Park
Research Institute for Natural Sciences
Hanyang University
Korea
baak@hanyang.ac.kr
Jung Rye
Lee
Department of Mathematics
Daejin University
Korea
jrlee@daejin.ac.kr
Hyers-Ulam stability
algebra- \(C^*\)-ternary ring
fixed point
quadratic functional equation
algebra-ternary Banach algebra
ternary quadratic derivation.
Article.5.pdf
[
[1]
T. Aoki , On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66
##[2]
A. Bodaghi, I. A. Alias, Approximate ternary quadratic derivation on ternary Banach algebras and \(C^*\)-ternary rings, Adv. Difference Equ., 2012 (2012), 1-9
##[3]
J. Diaz, B. Margolis , A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74 (1968), 305-309
##[4]
D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27 (1941), 222-224
##[5]
C. Park , Homomorphisms between Poisson \(JC^*\)-algebras, Bull. Braz. Math. Soc., 36 (2005), 79-97
##[6]
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300
##[7]
S. Shagholi, M. Eshaghi Gordji, M. B. Savadkouhi, Stability of ternary quadratic derivation on ternary Banach algebras, J. Comput. Anal. Appl., 13 (2011), 1097-1105
##[8]
F. Skof, Propriet locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano, 53 (1983), 113-129
##[9]
S. M. Ulam, Problems in Modern Mathematics, Chapter V I. Science ed., Wiley, New York (1940)
]
A stronger inequality of Cîrtoaje's one with power exponential functions
A stronger inequality of Cîrtoaje's one with power exponential functions
en
en
In this paper, we will show that \(a^{2b} + b^{2a} + r (ab(a - b))^2 \leq 1 \) holds for all \(0 \leq a\) and \(0 \leq b\) with \(a + b = 1\)
and all \(0 \leq r \leq\frac{1}{2}\). This gives the first example of a stronger inequality of \(a^{2b} +b^{2a} \leq 1\).
224
230
Mitsuhiro
Miyagi
General Education
Ube National College of Technology
Japan
miyagi@ube-k.ac.jp
Yusuke
Nishizawa
General Education
Ube National College of Technology
Japan
yusuke@ube-k.ac.jp
Power-exponential function
monotonically decreasing function
monotonically increasing function.
Article.6.pdf
[
[1]
A. Coronel, F. Huancas , On the inequality \(a^{2a} +b^{2b} +c^{2c} \geq a^{2b} +b^{2c} +c^{2a}\) , Aust. J. Math. Anal. Appl., 9 (2012), 1-5
##[2]
V. Cîrtoaje, On some inequalities with power-exponential functions, JIPAM. J. Inequal. Pure Appl. Math., 10 (2009), 1-6
##[3]
V. Cîrtoaje, Proofs of three open inequalities with power-exponential functions, J. Nonlinear Sci. Appl., 4 (2011), 130-137
##[4]
L. Matejicka, Proof of one open inequality, J. Nonlinear Sci. Appl., 7 (2014), 51-62
##[5]
M. Miyagi, Y. Nishizawa, Proof of an open inequality with double power-exponential functions, J. Inequal. Appl., 2013 (2013), 1-11
##[6]
M. Miyagi, Y. Nishizawa, A short proof of an open inequality with power-exponential functions, Aust. J. Math. Anal. Appl., 11 (2014), 1-3
]
Hermite--Hadamard type inequalities for the product of (\(\alpha, m\))-convex functions
Hermite--Hadamard type inequalities for the product of (\(\alpha, m\))-convex functions
en
en
In the paper, the authors establish some Hermite-Hadamard type inequalities for the product of two (\(\alpha, m\))-
convex functions.
231
236
Hong-Ping
Yin
College of Mathematics
Inner Mongolia University for Nationalities
China
hongpingyin@qq.com
Feng
Qi
Department of Mathematics, College of Science
Tianjin Polytechnic University
China
qifeng618@gmail.com;qifeng618@hotmail.com
Hermite-Hadamard type inequality
product
(\(\alpha، m\))-convex function
Hölder inequality.
Article.7.pdf
[
[1]
R.-F. Bai, F. Qi, B.-Y. Xi , Hermite-Hadamard type inequalities for the m- and (\(\alpha,m\))-logarithmically convex functions, Filomat, 27 (2013), 1-7
##[2]
M. K. Bakula, M. E. Özdemir, J. Pečarić, Hadamard type inequalities for m-convex and (\(\alpha,m\))-convex functions, JIPAM, J. Inequal. Pure Appl. Math., 9 (2008), 1-12
##[3]
S. S. Dragomir, G. Toader, Some inequalities for m-convex functions, Studia Univ. Babeş-Bolyai Math., 38 (1993), 21-28
##[4]
V. G. Miheşan, A generalization of the convexity, Seminar on Functional Equations, Approx. Convex, Cluj-Napoca (1993)
##[5]
B. G. Pachpatte, On some inequalities for convex functions, RGMIA Res. Rep. Coll., Suppl., Art. 1, Available online at http://rgmia.org/v6(E).php. (2003)
##[6]
Y. Shuang, H.-P. Yin, F. Qi, Hermite-Hadamard type integral inequalities for geometric-arithmetically s-convex functions , Analysis (Munich), 33 (2013), 197-208
##[7]
G. Toader, Some generalizations of the convexity, Proceedings of the Colloquium on Approximation and Optimization, Univ. Cluj-Napoca, Cluj, (1985), 329-338
##[8]
B.-Y. Xi, F. Qi , Hermite-Hadamard type inequalities for functions whose derivatives are of convexities, Nonlinear Funct. Anal. Appl., 18 (2013), 163-176
##[9]
B.-Y. Xi, F. Qi, Some Hermite-Hadamard type inequalities for differentiable convex functions and applications, Hacet. J. Math. Stat., 42 (2013), 243-257
##[10]
B.-Y. Xi, F. Qi, Some inequalities of Hermite-Hadamard type for h-convex functions, Adv. Inequal. Appl., 2 (2013), 1-15
##[11]
B.-Y. Xi, Y. Wang, F. Qi , Some integral inequalities of Hermite-Hadamard type for extended (s;m)-convex functions, Transylv. J. Math. Mechanics, 5 (2013), 69-84
##[12]
T.-Y. Zhang, A.-P. Ji, F. Qi, Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means, Matematiche (Catania), 68 (2013), 229-239
]
Banach fixed point theorem for digital images
Banach fixed point theorem for digital images
en
en
In this paper, we prove Banach fixed point theorem for digital images. We also give the proof of a theorem
which is a generalization of the Banach contraction principle. Finally, we deal with an application of Banach
fixed point theorem to image processing.
237
245
Ozgur
Ege
Department of Mathematics
Celal Bayar University
Turkey
ozgur.ege@cbu.edu.tr
Ismet
Karaca
Departments of Mathematics
Ege University
Turkey
ismet.karaca@ege.edu.tr
Digital image
fixed point
Banach contraction principle
digital contraction.
Article.8.pdf
[
[1]
S. Banach, Sur les operations dans les ensembles abstraits et leurs applications aux equations integrales, Fund. Math., 3 (1922), 133-181
##[2]
G. Bertrand, Simple points, topological numbers and geodesic neighborhoods in cubic grids, Pattern Recognition Letters, 15 (1994), 1003-1011
##[3]
G. Bertrand, R. Malgouyres, Some topological properties of discrete surfaces, J. Math. Imaging Vis., 20 (1999), 207-221
##[4]
L. Boxer, Digitally continuous functions, Pattern Recognition Letters, 15 (1994), 833-839
##[5]
L. Boxer, A classical construction for the digital fundamental group, J. Math. Imaging Vis., 10 (1999), 51-62
##[6]
L. Boxer, Properties of digital homotopy, J. Math. Imaging Vis., 22 (2005), 19-26
##[7]
L. Boxer, Digital products, wedges and covering spaces, J. Math. Imaging Vis., 25 (2006), 159-171
##[8]
L. Boxer, Continuous maps on digital simple closed curves, Appl. Math., 1 (2010), 377-386
##[9]
O. Ege, I. Karaca , Fundamental properties of simplicial homology groups for digital images, American Journal of Computer Technology and Application, 1 (2013), 25-42
##[10]
O. Ege, I. Karaca, Lefschetz Fixed Point Theorem for Digital Images, Fixed Point Theory Appl., 2013 (2013), 1-13
##[11]
O. Ege, I. Karaca, Applications of the Lefschetz Number to Digital Images, Bull. Belg. Math. Soc. Simon Stevin, 21 (2014), 823-839
##[12]
S. E. Han , An extended digital \((k_0; k_1)\)-continuity, J. Appl. Math. Comput., 16 (2004), 445-452
##[13]
S. E. Han, Minimal simple closed 18-surfaces and a topological preservation of 3D surfaces, Inform. Sci., 176 (2006), 120-134
##[14]
S. E. Han, Connected sum of digital closed surfaces, Inform. Sci., 176 (2006), 332-348
##[15]
G. T. Herman, Oriented surfaces in digital spaces , CVGIP: Graphical Models and Image Processing, 55 (1993), 381-396
##[16]
Sh. Jain, Sh. Jain, L. B. Jain, On Banach contraction principle in a cone metric space, J. Nonlinear Sci. Appl., 5 (2012), 252-258
##[17]
M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 1-8
##[18]
I. Karaca, O. Ege, Some results on simplicial homology groups of 2D digital images, Int. J. Inform. Computer Sci., 1 (2012), 198-203
##[19]
T. Y. Kong, A digital fundamental group, Computers and Graphics, 13 (1989), 159-166
##[20]
R. Malgouyres, G. Bertrand, A new local property of strong n-surfaces, Pattern Recognition Letters, 20 (1999), 417-428
##[21]
A. Rosenfeld, Digital topology, Amer. Math. Monthly, 86 (1979), 76-87
##[22]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings , Nonlinear Anal., 75 (2012), 2154-2165
##[23]
W. Shatanawi, H. K. Nashine, A generalization of Banach's contraction principle for nonlinear contraction in a partial metric space, J. Nonlinear Sci. Appl., 5 (2012), 37-43
]
Local convergence of deformed Halley method in Banach space under Holder continuity conditions
Local convergence of deformed Halley method in Banach space under Holder continuity conditions
en
en
We present a local convergence analysis for deformed Halley method in order to approximate a solution
of a nonlinear equation in a Banach space setting. Our methods include the Halley and other high order
methods under hypotheses up to the first Fréchet-derivative in contrast to earlier studies using hypotheses
up to the second or third Fréchet-derivative. The convergence ball and error estimates are given for these
methods. Numerical examples are also provided in this study.
246
254
Ioannis K.
Argyros
Department of Mathematical Sciences
Cameron University
USA
iargyros@cameron.edu
Santhosh
George
Department of Mathematical and Computational Sciences
India-575 025
sgeorge@nitk.ac.in
Chebyshev method
Banach space
convergence ball
local convergence.
Article.9.pdf
[
[1]
S. Amat, S. Busquier, J. M. Gutiérrez , Geometric constructions of iterative functions to solve nonlinear equations, J. Comput. Appl. Math., 157 (2003), 197-205
##[2]
I. K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach spaces, J. Math. Anal. Appl., 20 (2004), 373-397
##[3]
I. K. Argyros, Computational theory of iterative methods, Series: Studies in Computational Mathematics, 15, Editors: C. K. Chui and L. Wuytack, Elsevier Publ. Co. , New York, U.S.A (2007)
##[4]
I. K. Argyros, Quadratic equations and applications to Chandrasekhar's and related equations, Bull. Austral. Math. Soc., 32 (1985), 275-292
##[5]
I. K. Argyros, S. Hilout , Numerical methods in Nonlinear Analysis, World Scientific Publ. Comp., New Jersey (2013)
##[6]
I. K. Argyros, S. Hilout , Weaker conditions for the convergence of Newton's method, J. Complexity, 28 (2012), 364-387
##[7]
V. Candela, A. Marquina, Recurrence relations for rational cubic methods I: The Halley method, Computing, 44 (1990), 169-184
##[8]
V. Candela, A. Marquina, Recurrence relations for rational cubic methods II: The Chebyshev method, Computing, 45 (1990), 355-367
##[9]
C. Chun, P. Stanica, B. Neta , Third order family of methods in Banach spaces, Computer Math. Appl., 61 (2011), 1665-1675
##[10]
J. M. Gutiérrez, M. A. Hernández, Recurrence relations for the super-Halley method, Computers Math. Appl., 36 (1998), 1-8
##[11]
J. M. Gutiérrez, M. A. Hernández, Third-order iterative methods for operators with bounded second derivative, J. Comput. Appl. Math., 82 (1997), 171-183
##[12]
M. A. Hernández, M. A. Salanova, Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method, J. Comput. Appl. Math., 126 (2000), 131-143
##[13]
M. A. Hernández, Chebyshev's approximation algorithms and applications, Computers Math. Appl., 41 (2001), 433-455
##[14]
L. V. Kantorovich, G. P. Akilov, Functional Analysis, Pergamon Press, Oxford (1982)
##[15]
J. M. Ortega, W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables , Academic press, New York (1970)
##[16]
P. K. Parida, D. K. Gupta, Recurrence relations for semi-local convergence of a Newton-like method in Banach spaces, J. Math. Anal. Appl., 345 (2008), 350-361
##[17]
Y. Zhao, Q. Wu, Newton-Kantorovich theorem for a family of modified Halley's method under Holder continuity conditions in Banach space, Appl. Math. Comput., 202 (2008), 243-251
]
Two different distributions of limit cycles in a quintic system
Two different distributions of limit cycles in a quintic system
en
en
In this paper, the conditions for bifurcations of limit cycles from a third-order nilpotent critical point in a
class of quintic systems are investigated. Treaty the system coefficients as parameters, we obtain explicit
expressions for the first fourteen quasi Lyapunov constants. As a result, fourteen or fifteen small amplitude
limit cycles with different distributions could be created from the third-order nilpotent critical point by two
different perturbations.
255
266
Hongwei
Li
School of Science
Linyi University
China
hongweifx@163.com
Yinlai
Jin
School of Science
Linyi University
China
jinyinlai@sina.com
Third-order nilpotent critical point
center-focus problem
bifurcation of limit cycles
quasi-Lyapunov constant.
Article.10.pdf
[
[1]
M.J. Alvarez, A. Gasull , Momodromy and stability for nilpotent critical points, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 15 (2005), 1253-1265
##[2]
N. N. Bautin , On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type, American Math. Soc. Translation, 1954 (1954), 1-19
##[3]
J. Chavarriga, I. García, J. Giné, Integrability of centers perturbed by quasi–homogeneous polynomials, J. Math. Anal. Appl., 211 (1997), 268-278
##[4]
A. Gasull, J. Torregrosa, A new algorithm for the computation of the Lyapunov constans for some degenerated critical points, Nonlin. Anal.: Proc. IIIrd World Congress on Nonlinear Analysis, 47 (2001), 4479-4490
##[5]
W. Huang, A. Chen, Bifurcation of limit cycles and isochronous centers for a quartic system, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 23 (2013), 1-10
##[6]
Y. Liu, J. Li , On third-order nilpotent critical points: integral factor method, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 21 (2011), 1293-1309
##[7]
F. Li, Y. Liu, H. Li, Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov system, Math. Comput. Simulation, 81 (2011), 2595-2607
##[8]
F. Li, J. Qiu, J. Li, Bifurcation of limit cycles, classification of centers and isochronicity for a class of non-analytic quintic systems, Nonlinear Dynamics, 76 (2014), 183-197
##[9]
F. Li, M. Wang, Bifurcation of limit cycles in a quintic system with ten parameters, Nonlinear Dynamics, 71 (2013), 213-222
##[10]
F. Li, Y. Wu , Center conditions and limit cycles for a class of nilpotent-Poincar systems, Appl. Math. Comput, 243:2 (2014), 114-120
##[11]
J. Qiu, F. Li, Two kinds of bifurcation phenomena in a quartic system, Adv. Difference Equ., 2015 (2015), 13662-015
##[12]
P. Yu, Y. Tian, Twelve limit cycles around a singular point in a planar cubic-degree polynomial, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 2690-2705
]
Difference equations involving causal operators with nonlinear boundary conditions
Difference equations involving causal operators with nonlinear boundary conditions
en
en
In this paper, we investigate nonlinear boundary problems for difference equations with causal operators.
Our boundary condition is given by a nonlinear function, and more general than ones given before. By
using the method of upper and lower solutions coupled with the monotone iterative technique, criteria on
the existence of extremal solutions are obtained, an example is also presented.
267
274
Wenli
Wang
Department of Information Engineering
China University of Geosciences Great Wall College
People's Republic of China
emilyzh@163.com
Jingfeng
Tian
College of Science and Technology
North China Electric Power University
People's Republic of China
tianjfhxm_ncepu@163.com
Causal operators
monotone iterative technique
upper and lower solutions
extremal solutions.
Article.11.pdf
[
[1]
R. P. Agarwal, D. O'Regan, P. J. Y. Wong , Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, (1999)
##[2]
C. Corduneanu, Some existence results for functional equations with causal operators, Nonlinear Anal., 47 (2001), 709-716
##[3]
Z. Drici, F. A. McRae, J. Vasundhara Devi, Differential equations with causal operators in a Banach space, Nonlinear Anal., 62 (2005), 301-313
##[4]
Z. Drici, F. A. McRae, J. Vasundhara Devi , Monotone iterative technique for periodic boundary value problems with causal operators, Nonlinear Anal., 64 (2006), 1271-1277
##[5]
X. Dong, Z. Bai, Positive solutions of fourth-order boundary value problem with variable parameters, J. Nonlinear Sci. Appl., 1 (2008), 21-30
##[6]
F. Geng, Differential equations involving causal operators with nonlinear periodic boundary conditions , Math. Comput. Model., 48 (2008), 859-866
##[7]
L. Hu, H. Xia, Global asymptotic stability of a second order rational difference equation, Appl. Math. Comput., 233 (2014), 377-382
##[8]
T. Jankowski, Boundary value problems for difference equations with causal operators, Appl. Math. Comput., 218 (2011), 2549-2557
##[9]
T. Jankowski , Existence of solutions for a coupled system of difference equations with causal operators, Appl. Math. Comput., 219 (2013), 9348-9355
##[10]
V. Lakshmikantham, S. Leela, Z. Drici, F. A. McRae, Theory of causal differential equations , World Scientific Press, Paris (2009)
##[11]
J. A. Nanware, D. B. Dhaigude, Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions, J. Nonlinear Sci. Appl., 7 (2014), 246-254
##[12]
D. O'Regan, A. Orpel, Fixed point and variational methods for certain classes of boundary-value problems, Appl. Anal., 92 (2013), 1393-1402
##[13]
P. Y. H. Pang, R. P. Agarwal , Periodic boundary value problems for first and second order discrete system, Math. Comput. Model., 16 (1992), 101-112
##[14]
I. P. Stavroulakis , Oscillation criteria for delay and difference equations with non-monotone arguments, Appl. Math. Comput., 226 (2014), 661-672
##[15]
P. Wang, S. Tian, Y. Wu, Monotone iterative method for first-order functional difference equations with nonlinear boundary value conditions, Appl. Math. Comput., 203 (2008), 266-272
##[16]
P. Wang, M. Wu, Oscillation of certain second order nonlinear damped difference equations with continuous variable, Appl. Math. Lett., 20 (2007), 637-644
##[17]
P. Wang, M. Wu, Y. Wu , Practical stability in terms of two measures for discrete hybrid systems, Nonlinear Anal. Hybrid Syst., 2 (2008), 58-64
##[18]
P. Wang, J. Zhang , Monotone iterative technique for initial-value problems of nonlinear singular discrete systems, J. Comput. Appl. Math., 221 (2008), 158-164
##[19]
X. Xu, D. Jiang, W. Hu, D. O'Regan , Positive properties of Green's function for three-point boundary value problems of nonlinear fractional differential equations and its applications, Appl. Anal., 91 (2012), 323-343
##[20]
W. Zhuang, Y. Chen, S. Cheng, Monotone methods for a discrete boundary problem, Comput. Math. Appl., 32 (1996), 41-49
]
Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres
Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres
en
en
The null curves on 3-null cone have the applications in the studying of horizon types. Via the pseudo-scalar
product and Frenet equations, the differential geometry of null curves on 3-null cone is obtained. In the local
sense, the curvature describes the contact of submanifolds with pseudo-spheres. We introduce the geometric
properties of the null curves on 3-null cone and unit semi-Euclidean 3-spheres, respectively. On the other
hand, we give the existence conditions of null Bertrand curves on 3-null cone and unit semi-Euclidean
3-spheres.
275
284
Jianguo
Sun
School of Science
China University of Petroleum (east China)
P. R. China
sunjg616@163.com
Donghe
Pei
School of Mathematics and Statistics
Northeast Normal University
P. R. China
peidh340@nenu.edu.cn
Null Bertrand curve
AW(k)-type curve
Frenet frame
null cone.
Article.12.pdf
[
[1]
K. Arslan, C. Özgür , Curves and surfaces of AW(k)-type, in: Defever, F, J. M. Morvan, I. V. Woestijne, L. Verstraelen, G. Zafindratafa, (Eds.), Geometry and Topology of Submanifolds, World Scientific (1999)
##[2]
H. Balgetir, M. Bektaş, M. Ergüt , Bertrand cuves for nonnull curves in 3 dimensional Lorentzian space , Hadronic Journal, 27 (2004), 229-236
##[3]
H. Balgetir, M. Bektaş, J. Inoguchi, Null Bertrand curves in Minkowski 3 space and their characterizations, Note di Matematica, 23 (2004), 7-13
##[4]
M. Barros, A. Ferrández, Null scrolls as solutions of a sigma model, J. Phys. A-Math. thoer., 45 (2012), 1-12
##[5]
M. Campanelli, C. O. Lousto, Second order gauge invariant gravitational perturbations of a Kerr black hole, Phys. Rev. D, 59 (1999), 1-16
##[6]
K. L. Duggal, D. H. Jin , Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, (2007)
##[7]
S. Ersoy, A. Inalcik, On the generalized timelike Bertrand curves in 5-dimensional Lorentzian space, Differential Geom.-Dynamical Systems, 13 (2011), 78-88
##[8]
A. Ferrández, A. Giménez, P. Lucas, Geometrical particle models on 3D null curves, Phys. Lett. B, 543 (2002), 311-317
##[9]
M. Göçmen, S. Keleş, , arXiv preprint , arXiv:1104.3230 (2011)
##[10]
K. Ilarslan, Ö. Boyacıoğlu, Position vectors of a timelike and a null helix in Minkowski 3-space, Chaos Solitons Fractals, 38 (2008), 1383-1389
##[11]
L. L. Kong, D. H. Pei , On spacelike curves in hyperbolic space times sphere, Int. J. Geom. Methods Mod. Phys., 11 (2014), 1-12
##[12]
C. Kozameh, P. W. Lamberti, O. Reula, Global aspects of light cone cuts, J. Math. Phys., 32 (1991), 3423-3426
##[13]
M. Külahcı, M. Ergüt , Bertrand curves of AW(k)-type in Lorentzian space, Nonlinear Anal., 70 (2009), 1725-1731
##[14]
M. Külahcı, M. Bektaş, M. Ergüt , Curves of AW(k)-type in 3-dimensional null cone, Phys. Lett. A, 371 (2007), 275-277
##[15]
P. Lucas, J. A. Ortega-Yagües, Bertrand curves in the three-dimensional sphere, J. Geom. Phys., 62 (2012), 1903-1914
##[16]
B. O’Neill , Semi-Riemannian Geomerty with applications to relativity, Academic press, London (1983)
##[17]
A. Neraessian, E. Ramos, Massive spinning particles and the geometry of null curves, Phys. Lett. B, 445 (1998), 123-128
##[18]
C. Özgür, F. Gezgin, On some curves of AW(k)-type, Differential Geom.-Dynamical systems, 7 (2005), 74-80
##[19]
H. B. Oztekin, Weakened Bertrand curves in the Galilean space G3, J. Adv. Math. Studies, 2 (2009), 69-76
##[20]
L. R. Pears, Bertrand curves in Riemannian space, J. London Math. Soc., 1 (1935), 180-183
##[21]
S. G. Papaioannou, D. Kiritsis , An application of Bertrand curves and surfaces to CADCAM , Comput. Aided Geom. Design, 17 (1985), 348-352
##[22]
R. A. Penrose, Remarkable property of plane waves in general relativity, Rev. Modern Phys., 37 (1965), 215-220
##[23]
J. G. Sun, D. H. Pei, Null Cartan Bertrand curves of AW(k)-type in Minkowski 4-space, Phys. Lett. A, 376 (2012), 2230-2233
##[24]
J. G. Sun, D. H. Pei, Families of Gauss indicatrices on Lorentzian hypersurfaces in pseudo-spheres in semi- Euclidean 4 space, J. Math. Anal. Appl., 400 (2013), 133-142
##[25]
J. G. Sun, D. H. Pei, Null surfaces of null curves on 3-null cone, Phys. Lett. A, 378 (2014), 1010-1016
##[26]
G. H. Tian, Z. Zhao, C. B. Liang, Proper acceleration' of a null geodesic in curved spacetime, Classical Quant. Grav., 20 (2003), 1-4329
##[27]
M. Y. Yilmaz, M. Bektaş, General properties of Bertrand curves in Riemann-Otsuki space, Nonlinear Anal., 69 (2008), 3225-3231
]