]>
2014
7
3
ISSN 2008-1898
78
Fixed point results for \(GP_{(\Lambda,\Theta)}\)-contractive mappings
Fixed point results for \(GP_{(\Lambda,\Theta)}\)-contractive mappings
en
en
In this paper, we introduce new notions of \(GP\)-metric space and \(GP_{(\Lambda,\Theta)}\)-contractive mapping and then
prove some fixed point theorems for this class of mappings. Our results extend and generalized Banach
contraction principle to \(GP\)-metric spaces. An example shows the usefulness of our results.
150
159
Vahid
Parvaneh
Department of Mathematics, College of Science
Gilan-E-Gharb Branch, Islamic Azad University
Iran
vahid.parvaneh@kiau.ac.ir
Peyman
Salimi
Young Researchers and Elite Club, Rasht Branch
Islamic Azad University
Iran
salimipeyman@gmail.com
Pasquale
Vetro
Dipartimento di Matematica e Informatica
Universita degli Studi di Palermo
Italy
vetro@math.unipa.it
Akbar Dehghan
Nezhad
Department of Mathematics
Yazd University
Iran
anezhad@yazd.ac.ir
Stojan
Radenović
Faculty of Mathematics
University of Belgrade
Serbia
radens@beotel.net
\(GP\)-metric spaces
\(GP_(\Lambda
\Theta)\)-contractive mappings
\(O-GP\)-continuous.
Article.1.pdf
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[1]
M. Abbas, T. Nazir, P. Vetro, Common fixed point results for three maps in G-metric spaces, Filomat, 25:4 (2011), 1-17
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H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topology Appl., 159 (2012), 3234-3242
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H. Aydi, E. Karapinar, P. Salimi , Some fixed point results in GP-metric spaces, J. Appl. Math., Article ID 891713. (2012)
##[4]
H. Aydi, W. Shatanawi, C. Vetro , On generalized weak G-contraction mapping in G-metric spaces, Comput. Math. Appl., 62 (2011), 4223-4229
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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: 124 (2012)
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S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales , Fund. Math., 3 (1922), 133-181
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V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory Appl., 2012:105 (2012)
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B. Damjanovic, B. Samet, C. Vetro, Common fixed point theorems for multi-valued maps, Acta Math. Sci. Ser. B Engl. Ed., 32 (2012), 818-824
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C. Di Bari, P. Vetro, Fixed points for weak \(\phi\)-contractions on partial metric spaces, Int. J. of Engineering, Contemporary Mathematics and Sciences, 1 (2011), 5-13
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C. Di Bari, Z. Kadelburg, H. Nashine, S. Radenović, Common fixed points of g-quasicontractions and related mappings in 0-complete partial metric spaces, Fixed Point Theory Appl., 2012:113 (2012)
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R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc., 60 (1968), 71-76
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V. La Rosa, P. Vetro, Fixed points for Geraghty-contractions in partial metric spaces, J. Nonlinear Sci. Appl., 7 (1) (2014), 1-10
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S. G. Matthews, Partial metric topology , in: Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 728 (1994), 183-197
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D. Miheţ , Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces , J. Nonlinear Sci. Appl., 6 (1) (2013), 35-40
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Z. Mustafa, H. Obiedat, A fixed point theorem of Reich in G-metric spaces, CUBO, 12 (1) (2010), 83-93
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Z. Mustafa, W. Shatanawi, M. Bataineh, Existence of fixed point results in G-metric spaces, Int. J. Math. Math. Sci., Article ID 283028, 2009 (2009), 1-10
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Z. Mustafa, B. Sims, Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl., Article ID 917175, 2009 (2009), 1-10
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D. Paesano, P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920
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S. Radenović, P. Salimi, S. Pantelic, J. Vujaković, A note on some tripled coincidence point results in G-metric spaces, Int. J. Math. Sci and Engg. Appls.(November 2012), 6 (2012), 23-38
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S. Reich, Kannan's fixed point theorem, Boll. Un. Mat. Ital., 4 (1971), 1-11
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I. A. Rus, Fixed point theory in partial metric spaces, Anal. Univ. de Vest, Timisoara, Seria Matematică-Informatică, 46 (2008), 141-160
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B. Samet, M. Rajović, R. Lazović, R. Stoiljković, Common fixed point results for nonlinear contractions in ordered partial metric spaces , Fixed Point Theory Appl., 2011:71 (2011)
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B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
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R. Saadati, S. M. Vaezpour, P. Vetro, B. E. Rhoades , Fixed point theorems in generalized partially ordered G-metric spaces , Mathematical and Computer Modelling., 52 (2010), 797-801
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T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), 1861-1869
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C. Vetro, F. Vetro, Common fixed points of mappings satisfying implicit relations in partial metric spaces, J. Nonlinear Sci. Appl. , 6 (3) (2013), 152-161
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F. Vetro, On approximating curves associated with nonexpansive mappings, Carpathian J. Math., 27 (2011), 142-147
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M. R. A. Zand, A. D. Nezhad , A generalization of partial metric spaces, Journal of Contemporary Applied Mathematics., 24 (2011), 86-93
]
Bifurcation in a variational problem on a surface with a distance constraint
Bifurcation in a variational problem on a surface with a distance constraint
en
en
We describe a variational problem on a surface of a Euclidean space under a distance constraint. We
provide sufficient and necessary conditions for the existence of bifurcation points, generalizing Skrypnik's
analog described in [P. Vyridis, Int. J. Nonlinear Anal. Appl. 2 (2011), 1-10]. The problem in local
coordinates corresponds to an elliptic boundary value problem.
160
167
Panayotis
Vyridis
Department of Physics and Mathematics
National Polytechnical Institute (I.P.N.)
Mexico
pvyridis@gmail.com
Calculus of Variations
Critical points
Bifurcation points
Distance function
Curvatures of a Surface
Boundary value problem for an elliptic PDE.
Article.2.pdf
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##[7]
P. Vyridis, Free and Constrained Equilibrium States in a Variational Problem on a Surface , , (to appear)
]
\(\alpha-\psi-\varphi\)-contractive mappings in ordered partial b-metric spaces
\(\alpha-\psi-\varphi\)-contractive mappings in ordered partial b-metric spaces
en
en
In this paper, we introduce the concept of \(\alpha-\psi-\varphi\)-contractive self mapping in complete ordered partial b-
metric space, and we study the existence of fixed points for such mappings under some conditions. Presented
theorems in this paper extend and generalize the results derived by Mustafa et al., also some examples are
given to illustrate the main results.
168
179
Aiman
Mukheimer
Department of Mathematics and General Sciences
Prince Sultan University
Saudi Arabia
mukheimer@psu.edu.sa
b-metric space
fixed point theory
contraction
partial metric space.
Article.3.pdf
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[1]
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H. Aydi, M. Bota, E. Karapinar, S. Mitrovic , A fixed point theorem for set valued quasi-contractions in b-metric spaces, Fixed Point Theory and its Applications, 2012:88 (2012), 1-8
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E. Karapinar, R. P. Agarwal , A note on Coupled fixed point theorems for \(\alpha-\psi\)-contractive-type mappings in partially ordered metric spaces, Fixed Point Theory and Applications, 2013:216 (2013), 1-16
##[12]
A. Kaewcharoen, T. Yuying, Unique common fixed point theorems on partial metric spaces, Journal of Nonlinear Sciences and Applications, 7 (2014), 90-101
##[13]
E. Karapinar, B. Samet, Generalized \(\alpha-\psi\) contractive type mappings and related fixed point theorems with applications, Abstract and Applied Analysis, Art. ID 793486, 2012 (2012), 1-17
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K. Mehmet, H. Kiziltunc, On Some Well Known Fixed Point Theorems in b-Metric Spaces, Turkish Journal of Analysis and Number Theory, 1 (2013), 13-16
##[17]
Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Some common fixed point result in ordered partal b-metric spaces, Journal of Inequalities and Applications, 2013 (2013), 1-562
##[18]
H. Nashinea, M. Imdadb, M. Hasanc, Common fixed point theorems under rational contractions in complex valued metric spaces, Journal of Nonlinear Sciences and Applications, 7 (2014), 42-50
##[19]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\) -contactive type mappings, Nonlinear Analysis, 75 (2012), 2154-2165
##[20]
W. Shatanawia, H. Nashineb, A generalization of Banach's contraction principle for nonlinear contraction in a partial metric space, Journal of Nonlinear Sciences and Applications, 5 (2012), 37-43
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S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterranean Journal of Mathematics, doi:10.1007/s00009-013-0327-4 (2013)
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S. Singh, B. Chamola, Quasi-contractions and approximate fixed points, J. Natur. Phys. Sci., 16 (2002), 105-107
##[23]
C. Vetroa, F. Vetrob , Common fixed points of mappings satisfying implicit relations in partial metric spaces, Journal of Nonlinear Sciences and Applications, 6 (2013), 152-161
##[24]
H. Yingtaweesittikul , Suzuki type fixed point for generalized multi-valued mappings in b-metric spaces, Fixed Point Theory and Applications, 2013:215 (2013), 1-9
]
Modified Noor iterations with errors for nonlinear equations in Banach spaces
Modified Noor iterations with errors for nonlinear equations in Banach spaces
en
en
We introduce a new three step iterative scheme with errors to approximate the unique common fixed point
of a family of three strongly pseudocontractive (accretive) mappings on Banach spaces. Our results are
generalizations and improvements of results obtained by several authors in literature. In particular, they
generalize and improve the results of Mogbademu and Olaleru [A. A. Mogbademu and J. O. Olaleru, Bull.
Math. Anal. Appl., 3 (2011), 132-139], Xue and Fan [Z. Xue and R. Fan, Appl. Math. Comput., 206
(2008), 12-15] which is in turn a correction of Rafiq [A. Rafiq, Appl. Math. Comput., 182 (2006), 589-595].
180
187
G. A.
Okeke
Department of Mathematics, Faculty of Science
University of Lagos
Nigeria
gaokeke1@yahoo.co.uk
J. O.
Olaleru
Department of Mathematics, Faculty of Science
University of Lagos
Nigeria
olaleru1@yahoo.co.uk
Three-step iterative scheme with errors
Banach spaces
strongly pseudocontractive operators
unique common fixed point
strongly accretive.
Article.4.pdf
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A. A. Mogbademu, J. O. Olaleru, Modifed Noor iterative methods for a family of strongly pseudocontractive maps, Bulletin of Mathematical Analysis and Applications , 3 (2011), 132-139
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C. H. Morales, J. J. Jung, Convergence of path for pseudocontractive mappings in Banach spaces, Proc. Amer. Math. Soc., 120 (2000), 3411-3419
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H. K. Nashine, M. Imdad, M. Hasan, Common fixed point theorems under rational contractions in complex valued metric spaces, Journal of Nonlinear Science and Applications, 7 (2014), 42-50
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M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251 (2000), 217-229
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M. A. Noor , Three-step iterative algorithms for multi-valued quasi variational inclusions, J. Math. Anal. Appl., 255 (2001), 589-604
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M. A. Noor, Some developments in general variational inequalities, Appl. Math. Computation, 152 (2004), 199-277
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M. A. Noor, T. M. Rassias, Z. Y. Huang, Three-step iterations for nonlinear accretive operator equations, J. Math. Anal. Appl., 274 (2002), 59-68
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J. O. Olaleru, A. A. Mogbademu, On modified Noor iteration scheme for non-linear maps, Acta Math. Univ. Comenianae, 2 (2011), 221-228
##[19]
J. O. Olaleru, G. A. Okeke, Convergence theorems on asymptotically demicontractive and hemicontractive mappings in the intermediate sense, Fixed Point Theory and Applications, 2013 (2013), 1-352
##[20]
A. Rafiq , Modified Noor iterations for nonlinear equations in Banach spaces, Applied Mathematics and Computation, 182 (2006), 589-595
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G. S. Saluja, Convergence of implicit random iteration process with errors for a finite family of asymptotically quasi-nonexpansive random operators, J. Nonlinear Sci. Appl., 4 (2011), 292-307
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Y. G. Xu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl., 224 (1998), 91-101
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Z. Xue, R. Fan, Some comments on Noor's iterations in Banach spaces, Applied Mathematics and Computation, 206 (2008), 12-15
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K. S. Zazimierski, Adaptive Mann iterative for nonlinear accretive and pseudocontractive operator equations, Math. Commun., 13 (2008), 33-44
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H. Y. Zhou, Y. Jia, Approximation of fixed points of strongly pseudocontractive maps without Lipschitz assumptions, Proc. Amer. Math. Soc., 125 (1997), 1705-1709
]
Modeling the treatment of tumor cells in a solid tumor
Modeling the treatment of tumor cells in a solid tumor
en
en
It is well known that the theory of differential equations and some software packages are important tools
for solving several actual problems from different real world domains.
The novelty of this paper is the fact that the mathematical model of evolution of leukemic cells is adapted
to the case of tumor cells, from a solid tumor, together with the treatment of the solid homogeneous tumor.
Using the paper Dingli and Michor [D. Dingli, F. Michor, STEM-CELLS, 24 (2006), 2603-2610], we
consider the model of evolution of a leukemic population for the case of solid tumors.
188
195
Lorand
Parajdi
Faculty of Mathematics and Computer Science
Romania
lorand@cs.ubbcluj.ro
Cauchy problem
mathematical model
solid tumor
tumor cells
system of differential equations.
Article.5.pdf
[
[1]
S. Arghirescu, A. Cucuianu, R. Precup, M. Şerban, Mathematical Modeling of Cell Dynamics after Allogeneic Bone Marrow Transplantation in Acute Myeloid Leukemia , Int. J. Biomath., 5 (2012), 1-18
##[2]
A. Cucuianu, R. Precup, , A Hypothetical-Mathematical Model of Acute Myeloid Leukaemia Pathogenesis , Comput. Math. Methods Med., 11 (2010), 49-65
##[3]
D. Dingli, F. Michor , Successful Therapy Must Eradicate Cancer Stem Cells, STEM-CELLS, 24 (2006), 2603-2610
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J. Guckenheimer, P. Holmes, Nonlineat Oscillations, Dynamical Systems, and Bifurcation of Vector Fields , Springer-Verlag, (1983)
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C. Iancu, I. A. Rus, Mathematical Modeling, Transilvania Press, Cluj-Napoca (1996)
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S. Lynch, Dynamical Systems with Applications using Maple, second edition, Birkhäuser , Boston (2009)
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L. Preziosi , Cancer modelling and simulation, Ed. Chapman & Hall/CRC, (2003)
##[8]
R. Precup, M. A. Şerban, D. Trif , Asymptotic stability for cell dynamics after bone marrow transplantation, The 8th Joint Conference on Mathematics and Computer Science, Komarno, Slovakia, , (2010), 1-11
##[9]
R. W. Shonkwiler, J. Herod, Mathematical Biology, Ed. Springer, (2009)
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Z. Zeng , Scientific Computing with Maple Programming, , (2001)
]
A fixed point theorem for (\(\varphi,L\))-weak contraction mappings on a partial metric space
A fixed point theorem for (\(\varphi,L\))-weak contraction mappings on a partial metric space
en
en
In this paper, we explore (\(\varphi,L\))-weak contractions of Berinde by obtaining Suzuki-type fixed point results.
Thus, we obtain generalized fixed point results for Kannan's, Chatterjea's and Zamfirescu's mappings on a
0-complete partial metric space. In this way we obtain very general fixed point theorems that extend and
generalize several related results from the literature.
196
204
Ali
Erduran
Department of Mathematics, Faculty of Arts and Sciences
Kirikkale University
Turkey
ali.erduran1@yahoo.com
Z.
Kadelburg
Faculty of Mathematics
University of Belgrade
Serbia
kadelbur@matf.bg.ac.rs
H. K.
Nashine
Department of Mathematics
Disha Institute of Management and Technology
India
drhknashine@gmail.com;hemantnashine@gmail.com
C.
Vetro
Dipartimento di Matematica e Informatica
Universita degli Studi di Palermo
Italy
calogero.vetro@unipa.it
(\(\varphi
L\))-weak contraction
partial metric
0-complete space
Article.6.pdf
[
[1]
M. Abbas, P. Vetro, S. H. Khan, On fixed points of Berinde's contractive mappings in cone metric spaces, Carpathian J. Math., 26 (2010), 121-133
##[2]
T. Abdeljawad, E. Karapinar, K. Taş, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011), 1900-1904
##[3]
I. Altun, Ö. Acar, Fixed point theorems for weak contractions in the sense of Berinde on partial metric spaces, Topology Appl., 159 (2012), 2642-2648
##[4]
I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-10
##[5]
I. Altun, F. Sola, H. Simsek , Generalized contractions on partial metric spaces, Topology Appl., 157 (2010), 2778-2785
##[6]
I. Altun, A. Erduran, A Suzuki type fixed-point theorem, Intern. J. Math. Math. Sci., 2011 (2011), 1-9
##[7]
G. V. R. Babu, M. L. Sandhya, M. V. R. Kameswari, A note on fixed point theorem of Berinde on weak contractions, Carpathian J. Math., 24 (2008), 8-12
##[8]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund Math., 3 (1922), 133-181
##[9]
V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum, 9 (2004), 43-53
##[10]
V. Berinde, On the approximation of fixed points of weak contractive mappings, Carpathian J. Math., 19 (2003), 7-22
##[11]
V. Berinde, Iterative Approximation of Fixed Points, Springer-Verlag, Berlin-Heidelberg (2007)
##[12]
V. Berinde, Approximating fixed points of weak \(\varphi\)-contractions using the Picard iteration, Fixed Point Theory, 4 (2003), 131-142
##[13]
V. Berinde, General constructive fixed point theorems for Ćirić-type almost contractions in metric spaces, Carpathian J. Math., 24 (2008), 10-19
##[14]
V. Berinde, Approximating common fixed points of noncommuting discontinuous weakly contractive mappings in metric spaces, Carpathian J. Math., 25 (2009), 13-22
##[15]
V. Berinde, Some remarks on a fixed point theorem for Ćirić-type almost contractions, Carpathian J. Math., 25 (2009), 157-162
##[16]
V. Berinde, Approximating common fixed points of noncommuting almost contractions in metric spaces, Fixed Point Theory, 11:2 (2010), 179-188
##[17]
V. Berinde, Common fixed points of noncommuting almost contractions in cone metric spaces, Math. Commun, 15 (2010), 229-241
##[18]
V. Berinde, Common fixed points of noncommuting discontinuous weakly contractive mappings in cone metric spaces , Taiwanese J. Math., 14:5 (2010), 1763-1776
##[19]
V. Berinde, M. Păcurar, Fixed points and continuity of almost contractions, Fixed Point Theory, 9 (2008), 23-34
##[20]
D. Dorić, Z. Kadelburg, S. Radenović , Edelstein-Suzuki-type fixed point results in metric and abstract metric spaces, Nonlinear Anal., 75 (2012), 1927-1932
##[21]
Y. Enjouji, M. Nakanishi, T. Suzuki , A generalization of Kannan's fixed point theorem, Fixed Point Theory Appl., 2009 (2009), 1-10
##[22]
N. Hussain, D. Dorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012 (2012), 1-12
##[23]
M. Imdad, A. Erduran, Suzuki-Type Generalization of Chatterjea Contraction Mappings on Complete Partial Metric Spaces, Journal of Operators, 2013 (2013), 1-5
##[24]
A. Kaewcharoen, T. Yuying, Unique common fixed point theorems on partial metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 90-101
##[25]
E. Karapinar, I. M. Erhan , Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24 (2011), 1894-1899
##[26]
M. Kikkawa, T. Suzuki, Some similarity between contractions and Kannan mappings, Fixed Point Theory Appl., 2008 (2008), 1-8
##[27]
M. Kikkawa, T. Suzuki , Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. , 69 (2008), 2942-2949
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]
Nonlinear conservation law model for production network considering yield loss
Nonlinear conservation law model for production network considering yield loss
en
en
A mathematical model describing yield loss in a production network has been introduced. Mathematical
properties of the continuum model are discussed. Existence, uniqueness and stability of the solution are
demonstrated through weak formulation and entropy criteria. Front tracking method is implemented to
construct approximate solutions. Estimates of the solutions are also provided.
205
217
Tanmay
Sarkar
Department of Mathematics
Indian Institute of Technology Madras
India
tanmaysemilo@gmail.com
S.
Sundar
Department of Mathematics
Indian Institute of Technology Madras
India
slnt@iitm.ac.in
Production system
conservation laws
yield loss
front tracking.
Article.7.pdf
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]
Positive periodic solution for a nonlinear neutral delay population equation with feedback control
Positive periodic solution for a nonlinear neutral delay population equation with feedback control
en
en
In this paper, sufficient conditions are investigated for the existence of positive periodic solution for a
nonlinear neutral delay population system with feedback control. The proof is based on the fixed-point
theorem of strict-set-contraction operators. We also present an example of nonlinear neutral delay population
system with feedback control to show the validity of conditions and efficiency of our results.
218
228
Payam
Nasertayoob
Department of Mathematics
Amirkabir University of Technology (Polytechnic)
Iran
nasertayoob@aut.ac.ir
S. Mansour
Vaezpour
Department of Mathematics
Amirkabir University of Technology (Polytechnic)
Iran
vaez@aut.ac.ir
Fixed point theory
neutral nonlinear equation
feedback control
strict-set-contraction.
Article.8.pdf
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