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FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION 被引量：3

FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION
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摘要 In this paper, we introduce new concepts of a-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from a-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 application to nonlinear fractional differential equation are given to illustrate the usability of the new theory. In this paper, we introduce new concepts of a-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from a-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 application to nonlinear fractional differential equation are given to illustrate the usability of the new theory.
作者 Dhananjay GOPAL Mujahid ABBAS Deepesh Kumar PATEL Calogero VETRO
机构地区 Department of Applied Mathematics&Humanities Department of Mathematics and Applied Mathematics Department of Mathematics Department of Mathematics Visvesvaraya National Institute of Technology Universita degli Studi di Palermo
出处 《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期957-970,共14页 数学物理学报（B辑英文版）
基金 the support of CSIR,Govt.of India,Grant No.-25(0215)/13/EMR-II
关键词 fixed points nonlinear fractional differential equations periodic points fixed points nonlinear fractional differential equations periodic points
分类号 O175 [理学—基础数学]
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参考文献22

  • 1Abbas M, All B, Romaguera S. Fixed and periodic points of generalized contractions in metric space. Fixed Point Theory Appl, 2013, 2013:243.
  • 2Baleanu 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.
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  • 5Caristi J. Fixed point theorems for mappings satisfying inwardness conditions. Trans Amer Math Soc, 1976, 215:241-251.
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  • 7Hardy G E, Rogers TD. A generalization of a fixed point theorem of Reich. Canadian Math Bul, 1973, 16:201-206.
  • 8Hussain N, Salimi P. Suzuki-Wardowski type fixed point theorems for a-GF-contractions. Taiwan Residents J Math, 2014, 18:1879-1895.
  • 9Jachymski J. The contraction principle for mapping on a metric space with a graph. Proc Amer Math Soc, 2008, 136:1359-1373.
  • 10Jeong G S, Rhoades B E. Maps for which F(T) = F(Tn). Fixed Point Theory Appl, 2005, 6:87- 131.

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Acta Mathematica Scientia
2016年 第3期

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