FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

doi:10.1016/S0252-9602(16)30052-2

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (3): 957-970.doi: 10.1016/S0252-9602(16)30052-2

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FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

Dhananjay GOPAL¹, Mujahid ABBAS², Deepesh Kumar PATEL³, Calogero VETRO⁴

1. Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat-395007, Gujarat, India;
2. Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria 0002, South Africa;Department of Mathematics, King AbdulAziz University, P. O. Box 80203 Jeddah 21589, Saudi Arabia;
3. Department of Mathematics Visvesvaraya National Institute of Technology, Nagpur-440010, Maharashtra, India;
4. Università degli Studi di Palermo, Dipartimento di Matematica e Informatica, Via Archirafi, 34-90123 Palermo, Italy

收稿日期:2015-08-26 修回日期:2015-12-06 出版日期:2016-06-25 发布日期:2016-06-25
通讯作者: Dhananjay GOPAL,E-mail:dg@ashd.svnit.ac.in,gopaldhananjay@yahoo.in E-mail:dg@ashd.svnit.ac.in,gopaldhananjay@yahoo.in
作者简介:Mujahid ABBAS,E-mail:Mujahid.Abbas@up.ac.za,abbas.muajahid@gmail.com;Deepesh Kumar PATEL,E-mail:deepesh456@gmail.com;Calogero VETRO,E-mail:calogero.vetro@unipa.it

FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

Dhananjay GOPAL¹, Mujahid ABBAS², Deepesh Kumar PATEL³, Calogero VETRO⁴

1. Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat-395007, Gujarat, India;
2. Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria 0002, South Africa;Department of Mathematics, King AbdulAziz University, P. O. Box 80203 Jeddah 21589, Saudi Arabia;
3. Department of Mathematics Visvesvaraya National Institute of Technology, Nagpur-440010, Maharashtra, India;
4. Università degli Studi di Palermo, Dipartimento di Matematica e Informatica, Via Archirafi, 34-90123 Palermo, Italy

Received:2015-08-26 Revised:2015-12-06 Online:2016-06-25 Published:2016-06-25
Contact: Dhananjay GOPAL,E-mail:dg@ashd.svnit.ac.in,gopaldhananjay@yahoo.in E-mail:dg@ashd.svnit.ac.in,gopaldhananjay@yahoo.in

摘要/Abstract

摘要：

In this paper, we introduce new concepts of α-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in[21, 22] and differ-ent from α-GF-contractions given in[8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an appli-cation to nonlinear fractional differential equation are given to illustrate the usability of the new theory.

关键词: fixed points, nonlinear fractional differential equations, periodic points

Abstract:

Key words: fixed points, nonlinear fractional differential equations, periodic points

中图分类号:

37C25

Dhananjay GOPAL, Mujahid ABBAS, Deepesh Kumar PATEL, Calogero VETRO. FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION[J]. 数学物理学报(英文版), 2016, 36(3): 957-970.

参考文献

[1] Abbas M, Ali B, Romaguera S. Fixed and periodic points of generalized contractions in metric space. Fixed Point Theory Appl, 2013, 2013: 243
[2] Baleanu D, Rezapour Sh, Mohammadi M. Some existence results on nonlinear fractional differential equa-tions. Philos Trans R Soc A, Math Phys Eng Sci, 2013, 371(1990): Article ID 20120144
[3] Banach S. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund Math, 1922, 3: 133-181
[4] Boyd D W, Wong J S. On nonlinear contractions. Proc Amer Math Soc, 1969, 20: 458-462
[5] Caristi J. Fixed point theorems for mappings satisfying inwardness conditions. Trans Amer Math Soc, 1976, 215: 241-251
[6] ?iri? Lj B. A generalization of Banach's contraction principle. Proc Amer Math Soc, 1974, 45: 267-273
[7] Hardy G E, Rogers T D. A generalization of a fixed point theorem of Reich. Canadian Math Bull, 1973, 16: 201-206
[8] Hussain N, Salimi P. Suzuki-Wardowski type fixed point theorems for α-GF-contractions. Taiwanese J Math, 2014, 18: 1879-1895
[9] Jachymski J. The contraction principle for mapping on a metric space with a graph. Proc Amer Math Soc, 2008, 136: 1359-1373
[10] Jeong G S, Rhoades B E. Maps for which F(T)=F(Tⁿ). Fixed Point Theory Appl, 2005, 6: 87-131
[11] Khan M S, Swaleh M, Sessa S. Fixed point theorems by altering distances between the points. Bull Aust Math Soc, 1984, 30: 1-9
[12] Kirk W A, Srinivasan P S, Veeramani P. Fixed points for mappings satisfying cyclical contractive condi-tions. Fixed Point Theory, 2003, 4: 79-89
[13] Lakshmikantham V, ?iri? Lj B. Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal, 2009, 70: 4341-4349
[14] Meir A, Keeler E. A theorem on contraction mappings. J Math Anal Appl, 1969, 28: 326-329
[15] Podlubny I. Fractional Differential Equations. Academic Press, 1999
[16] Ran A C M, Reurings M C B. A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc Amer Math Soc, 2004, 132: 1435-1443
[17] Reich S. Some remarks concerning contraction mappings. Canadian Math Bull, 1971, 14: 121-124
[18] Samet B, Vetro C, Vetro P. Fixed point theorems for α-ψ-contractive type mappings. Nonlinear Anal, 2012, 75: 2154-2165
[19] SgroiM, Vetro C.Multi-valued F-contractions and the solution of certain functional and integral equations. Filomat, 2013, 27: 1259-1268
[20] Suzuki T. A generalized Banach contraction principle that characterizes metric completeness. Proc Amer Math Soc, 2008, 136: 1861-1869
[21] Wardowski D. Fixed points of new type of contractive mappings in complete metric space. Fixed Point Theory Appl, 2012, doi:10.1186/1687-1812-2012-94
[22] Wardowski D, Van Dung N. Fixed points of F-weak contractions on complete metric space. Demonstratio Math, 2014, 47: 146-155

FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

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