]>
2008
1
3
ISSN 2008-1898
79
POSITIVE SOLUTIONS FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION
POSITIVE SOLUTIONS FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION
en
en
We investigate the positive solution of nonlinear fractional differential equation with semi-positive nonlinearity
\[
\begin{cases}
D^\alpha_{0^+}u(t) + f(t, u(t)) = 0,\,\,\,\,\, 0 < t < 1,\\
u(0) = u'(1) = u''(0) = 0
\end{cases}
\]
where \(2 < \alpha\leq 3\) is a real number, \(D^\alpha_{0^+}\) is the Caputo's differentiation, and
\(f : [0; 1] \times [0, \infty) \rightarrow (-\infty , \infty)\). By use of Krasnosel'skii fixed point theorem,
the existence results of positive solution are obtained.
123
131
TINGTING
QIU
Department of Mathematics, Shandong University of Science and Technology,Qingdao, 266510, PRC.
ZHANBING
BAI
Department of Mathematics, Shandong University of Science and Technology, Qingdao, 266510, PRC.
Fractional differential equation
Positive solution
Fixed-point theorem.
Article.1.pdf
[
[1]
Z. B. Bai , Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. , 311 (2005), 495-505
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A. Babakhani, V. D. Gejj , Existence of positive solutions of nonlinear fractional differential equations, J. Math. Anal. Appl., 278 (2003), 434-442
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D. Delbosco, L. Rodino , Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl., 204 (1996), 609-625
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A. M. A. El-Sayed , Nonlinear functional differential equations of arbitrary orders, Nonlinear Analysis TMA , 33 (1998), 181-186
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V. D. Gejji, A. Babakhani , Analysis of a system of fractional differential equations, J. Math. Anal. Appl., 293 (2004), 511-522
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A. A. Kilbas, O. I. Marichev, S. G. Samko , Fractional Integral and Derivatives (Theory and Applications), Gordon and Breach, Switzerland (1993)
##[7]
A. A. Kilbas, J. J. Trujillo, Differential equations of fractional order: methods, results and problems-I, Applicable Analysis, 78 (2001), 153-192
##[8]
A. A. Kilbas, J. J. Trujillo, Differential equations of fractional order: methods, results and problems-II, Applicable Analysis , 81 (2002), 435-493
##[9]
K. S. Miller , Fractional differential equations, J. Fract. Calc. , 3 (1993), 49-57
##[10]
K. S. Miller, B. Ross , An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York (1993)
##[11]
S. Q. Zhang, The existence of a positive solution for a nonlinear fractional differential equation, J. Math. Anal. Appl., 252 (2000), 804-812
##[12]
S. Q. Zhang , Existence of positive solution for some class of nonlinear fractional differential equations, J. Math. Anal. Appl. , 278 (2003), 136-148
##[13]
Q. L. Yao, Existence of positive solution for a third order three point boundary value problem with semipositone nonlinearity, Journal of Mathematical Research Exposition., 23 (2003), 591-596
]
CONVERGENCE OF FIXED POINT OF ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE MAPPINGS IN CONVEX METRIC SPACE
CONVERGENCE OF FIXED POINT OF ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE MAPPINGS IN CONVEX METRIC SPACE
en
en
In this paper, we give some necessary and sufficient conditions for
three-step iterative sequence with errors for asymptotically quasi-nonexpansive
type mapping converging to a fixed point in convex metric spaces. The results
presented in this paper extend the corresponding results of Kim et al. [9, 10] and
many others. Also the corresponding results in [1, 2, 3, 6, 12, 13, 14, 16, 18, 20]
are spcial cases of our results.
132
144
GURUCHARAN SINGH
SALUJA
Department of Mathematics & Information Technology, Govt. Nagarjun P.G. College of Science, Raipur (C.G.), India.
Asymptotically nonexpansive mapping
asymptotically nonexpansive type mapping
asymptotically quasi-nonexpansive type mapping
convex metric space
fixed point
three-step iterative process with errors.
Article.2.pdf
[
[1]
S. S. Chang , Some results for asymptotically pseudo-contractive mapping and asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 129(3) (2001), 845-853
##[2]
S. S. Chang , Iterative approximation problem of fixed points for asymptotically nonexpansive mappings in Banach spaces, Acta Math. Appl. , 24(2) (2001), 236-241
##[3]
S. S. Chang , On the approximating problem of fixed points for asymptotically nonexpansive mappings, Indian J. Pure and Appl., 32(9) (2001), 1-11
##[4]
S. S. Chang, J. K. Kim, D. S. Jin, Iterative sequences with errors for asymptotically quasi- nonexpansive type mappings in convex metric spaces , Archives of Inequality and Applications , 2 (2004), 365-374
##[5]
Y. J. Cho, H. Zhou, G. Guo , Weak and strong convergence theorems for three step iterations with errors for asymptotically nonexpansive mappings, Computers and Math. with Appl. , 47 (2004), 707-717
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M. K. Ghosh, L. Debnath, Convergence of Ishikawa iterates of quasi-nonexpansive mappings, J. Math. Anal. Appl. , 207 (1997), 96-103
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R. Glowinski, P. Le Tallec , Augmented Lagrangian Operator-Splitting Metods in Non-linear Mechanics, SIAM, Philadelphia (1989)
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K. Goebel, W. A. Kirk , A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. , 35 (1972), 171-174
##[9]
J. K. Kim, K. H. Kim, K. S. Kim , Convergence theorems of modiied three-step iterative sequences with mixed errors for asymptotically quasi-nonexpansive mappings in Banach spaces, PanAmerican Math. Jour., 14(1) (2004), 45-54
##[10]
J. K. Kim, K. H. Kim, K. S. Kim , Three-step iterative sequences with errors for asymptotically quasi-nonexpansive mappings in convex metric spaces , Nonlinear Anal. Convex Anal. RIMS Vol., 1365 (2004), 156-165
##[11]
W. A. Kirk , Fixed point theorems for non-lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math., 17 (1974), 339-346
##[12]
Q. H. Liu , Iterative sequences for asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. , 259 (2001), 1-7
##[13]
Q. H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings with error member, J. Math. Anal. Appl., 259 (2001), 18-24
##[14]
Q. H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings with error member of uniformly convex Banach spaces, J. Math. Anal. Appl. , 266 (2002), 468-471
##[15]
M. A. Noor , New approximation schemes for general variational inequalities, J. Math. Anal. Appl. , 251 (2000), 217-229
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W. V. Petryshyn, T. E. Williamson , Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings, J. Math. Anal. Appl. , 43 (1973), 459-497
##[17]
W. Takahashi, A convexity in metric space and nonexpansive mappings I, Kodai Math. Sem. Rep. , 22 (1970), 142-149
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B. L. Xu, M. A. Noor , Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 267 (2002), 444-453
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K. K. Tan, H. K. Xu , Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. , 178 (1993), 301-308
##[20]
K. K. Tan, H. K. Xu , Fixed point iteration processes for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 122 (1994), 733-739
]
IMPLICIT VARIATIONAL-LIKE INCLUSIONS INVOLVING GENERAL H eta-MONOTONE OPERATORS
IMPLICIT VARIATIONAL-LIKE INCLUSIONS INVOLVING GENERAL H eta-MONOTONE OPERATORS
en
en
145
154
M. ALIMOHAMMADY AND M.
ROOHI
Article.3.pdf
[
]
SOME PROPERTIES OF \(C\)-FRAMES OF SUBSPACES
SOME PROPERTIES OF \(C\)-FRAMES OF SUBSPACES
en
en
In [13] frames of subspaces extended to continuous version namely
\(c\)-frame of subspaces. In this article we consider to the relations between \(c\)-
frames of subspaces and local \(c\)-frames. Also in this article we give some important relation about duality and parseval \(c\)-frames of subspaces.
.
155
168
Mohammad Hasan
Faroughi
Faculty of Mathematical Science, University of Tabriz, Iran
Reza
Ahmadi
Faculty of Mathematical Science, University of Tabriz, Iran
Zahra
Afsar
Faculty of Mathematical Science, University of Tabriz, Iran
Operator
Hilbert space
Bessel sequences
Frame
frames of subspaces
c-frames of subspaces
Article.4.pdf
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[1]
H. Blocsli, F. Hlawatsch, H. G. Fichtinger, Frame-Theoretic analysis of oversampled filter bank, IEEE Trans. Signal Processing. , 46(12) (1998), 3256-3268
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E. J. Candes, D. L. Donoho , New tight frames of curvelets and optimal representation of objects with piecwise \(C^2\) singularities, Comm. Pure and App. Math. , 57(2), (2004), 219-266
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P. G. Casazza, G. Kutyniok , Frame of subspaces, Contemporery math., 345(1) (2004), 87-114
##[5]
P. G. Casazza, G. Kutyniok, S. Li, Fusion frames and Distributed Processing , Appl. Comput. Harmon. Anal., 114-132 (2008)
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P. G. Casazza, J. Kovacvic, Equal-norm tight frames with erasures, Adv. Comput. Math., 18(2-4) (2003), 387-430
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O. Christensen, An introduction to frames and Riesz bases, Birkhauser, Boston (2003)
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I. Daubechies, A. Grossmann, Y. Meyer, painless nonorthogonal Expansions, J. Math. Phys. , 27(5) (1986), 1271-1283
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S. Ali, Twareque, J.-P. Antoine, J.-P. Gazeau, Continuous frames in Hilbert spaces, Ann. physics , 222(1) (1993), 1-37
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P. Găvrţa , On the duality of fusion frames, J. math. Anal. Appl. , 333 (2007), 871-897
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B. Hassibi, B. Hochwald, A. Shokrollahi, W. Sweldens, representation theory for high-rate multiple-antenna code design., IEEE Trans. Inform. Theory. , 47(6) (2001), 2335-2367
##[13]
A. Najati, R. Rahimi, M. H. Faroughi , Continuous and discrete frames of subspaces in Hilbert spaces. , Southeast Asian Bulletin of Mathematics. , 32 (2008), 305-324
##[14]
Pedersen, K. Gert . , analysis now, Springer-Verlag, New York (1989)
##[15]
A. Rahimi, A. Najati, Y. N. Dehghan, Continuous frame in Hilbert spaces, Methods of Functional Analysis and Topology, 12(2) (2006), 170-182
]
VISCOSITY APPROXIMATION METHOD FOR NONEXPANSIVE NONSELF-MAPPING AND VARIATIONAL INEQUALITY
VISCOSITY APPROXIMATION METHOD FOR NONEXPANSIVE NONSELF-MAPPING AND VARIATIONAL INEQUALITY
en
en
Let \(E\) be a real reflexive Banach space which has uniformly Gâteaux
differentiable norm. Let \(K\) be aclosed convex subset of \(E\) which is also a sunny
nonexpansive retract of \(E\), and \(T : K \rightarrow E\) be nonexpansive mapping satisfying the weakly inward condition and \(F(T) = \{x \in K, Tx = x\} \neq\emptyset\), and
\(f : K \rightarrow K\) be a contractive mapping. Suppose that \(x_0 \in K,\quad \{x_n\}\) is defined
by
\[
\begin{cases}
x_{n+1} = \alpha_nf(x_n) + (1 - \alpha_n)((1 - \delta)x_n + \delta y_n)\\
y_n = P(\beta_nx_n + (1 - \beta_n)Tx_n),\quad n \geq 0,
\end{cases}
\]
where \(\delta \in (0; 1), \alpha_n, \beta_n \in [0; 1], P\) is sunny nonexpansive retractive from \(E\) into
\(K\). Under appropriate conditions, it is shown that \(\{x_n\}\) converges strongly to
a fixed point \(T\) and the fixed point solutes some variational inequalities. The
results in this paper extend and improve the corresponding results of [2] and
some others.
169
178
ZHENHUA
HE
Department of Mathematics, Honghe university, Mengzi, Yunnan, 661100, China.
CAN
CHEN
Department of Mathematics, Honghe university, Mengzi, Yunnan, 661100, China.
FENG
GU
Department of Mathematics, Hangzhou normal university, Zhejiang, 310036, China.
Strong convergence
Nonexpansive nonself-mapping
Viscosity approximation method
Uniformly Gâteaux differentiable norm
Variational inequality.
Article.5.pdf
[
[1]
S. S. Chang , Some problems and results in the study of nonlinear analysis, Nonlinear Anal., 30 (1997), 4197-4208
##[2]
Y. Song, R. Chen, Viscosity approximation methods for nonexpansive nonself-mappings, J. Math. Anal. Apple., 321 (2006), 316-326
##[3]
Tomonari Suzuki , Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces,, Fixed Point Theory and Applications, 1 (2005), 103-123
##[4]
W. Takahashi , Nonlinear Functional Analysis, Yokohama Publishers, Yokohama (2000)
##[5]
W. Takahashi, Y. Ueda , On Reich' s strong convergence for resolvents of accretive operators, J. Math. Anal. Appl. , 104 (1984), 546-553
##[6]
H. K. Xu, Viscosity approximation methods for nonexpansive mappings , J. Math. Anal. Apple., 298 (2004), 279-291
##[7]
H.-K. Xu, Approximating curves of nonexpansive nonself-mappings in Banach spaces , in: Mathematical Analysis, C.R.Acad. Sci. Paris, 325 (1997), 151-156
##[8]
Hong-Kun Xu , Iterative algorithms for nonlinear operators, J. London. Math. Soc., 2 (2002), 240-256
##[9]
Habtu Zegeye, Naseer Shahzad , Strong convergence theorems for a common zero of a finite family of m-accretive mappings, Nonlinear Anal., 66 (2007), 1161-1169
]
CONVERGENCE OF NEW MODIFIED TRIGONOMETRIC SUMS IN THE METRIC SPACE L
CONVERGENCE OF NEW MODIFIED TRIGONOMETRIC SUMS IN THE METRIC SPACE L
en
en
We introduce here new modified cosine and sine sums as
\(\frac{a_0}{ 2} + \sum^n_{ k=1} \sum^n_{ j=k} \triangle(a_j \cos jx)\)
and
\( \sum^n_{ k=1} \sum^n_{ j=k} \triangle(a_j \sin jx)\)
and study their integrability and \(L^1\)-convergence. The \(L^1\)-convergence of cosine
and sine series have been obtained as corollary. In this paper, we have been able
to remove the necessary and sufficient condition \(a_k \log k = o(1)\) as \(k \rightarrow\infty\) for
the \(L^1\)-convergence of cosine and sine series.
179
188
JATINDERDEEP
KAUR
School of Mathematics & Computer Applications, Thapar University Patiala(Pb.)-147004, INDIA.
S.S.
BHATIA
School of Mathematics & Computer Applications, Thapar University Patiala(Pb.)-147004, INDIA.
\(L^1\)-convergence
Dirichlet kernel
Fejer kernel
monotone sequence.
Article.6.pdf
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[1]
N. K. Bary, A treatise on trigonometric series, Vol II, Pergamon Press, London (1964)
##[2]
A. N. Kolmogorov, Sur l'ordere de grandeur des coefficients de la series de Fourier-Lebesque, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys., (1923), 83-86
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S. Sheng, The extension of the theorems of C.V. Stanojević and V.B. Stanojević , Proc. Amer. Math. Soc., 110 (1990), 895-904
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S. Sidon, Hinreichende Bedingungen für den Fourier-Charakter einer trigonometrischen Reihe, J. London Math Soc., 14 (1939), 158-160
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S. A. Teljakovskĭi, A sufficient condition of Sidon for the integrability of trigonometric series, Mat. Zametki, 14(3) (1973), 317-328
]
A CONTRACTION THEOREM IN MENGER PROBABILISTIC METRIC SPACES
A CONTRACTION THEOREM IN MENGER PROBABILISTIC METRIC SPACES
en
en
In this paper, we consider complete menger probabilistic quasi-
metric space and prove a common fixed point theorem for commuting maps in
this space.
189
193
S.
SHAKERI
Department of Mathematics Islamic Azad University-Ayatollah Amoly Branch Amol P. O. Box 678, Amol, Iran.
Probabilistic metric spaces
menger space
fixed point theorem
commuting maps
triangle norm.
Article.7.pdf
[
[1]
S. S. Chang,Y. J. Cho, S. M. Kang , Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, Inc., New York (2001)
##[2]
O. Hadžić, E. Pap, Fixed Point Theory in PM Spaces, Kluwer Academic Publishers, Dordrecht (2001)
##[3]
D. Miheţ, V. Radu , On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl., 343 (2008), 567-572
##[4]
B. Schweizer, A. Sklar , Probabilistic Metric Spaces, Elsevier, North Holand, New York (1983)
]
RELATED FIXED POINT THEOREMS IN FUZZY METRIC SPACES
RELATED FIXED POINT THEOREMS IN FUZZY METRIC SPACES
en
en
We prove a related fixed point Theorem for four mappings which
are not continuous in four fuzzy metric spaces, one of them is a sequentially
compact fuzzy metric space. Our Theorem in the metric version generalizes
Theorem 4 of [1]. Finally, We give a fuzzy version of Theorem 3 of [1].
194
202
K. P. R.
RAO
Dept. of Applied Mathematics, Acharya Nagarjuna, University-Nuzvid Campus, NUZVID-521 201, Krishna Dt., A.P., INDIA.
ABDELKRIM
ALIOUCHE
Department of Mathematics, University of Larbi Ben M' Hidi, Oum-El-Bouaghi, 04000, Algeria.
G. RAVI
BABU
Dept. of Applied Mathematics, Acharya Nagarjuna, University-Nuzvid Campus, NUZVID-521 201, Krishna Dt., A.P., INDIA.
Fuzzy metric space
implicit relation
sequentially compact Fuzzy metric space
related fixed point.
Article.8.pdf
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[1]
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]