Coupled fixed point theorems for rational type contractions via C-class functions

Document Type : Research Paper

Authors
Arslan Hojat Ansari 1
Bahman Moeini 2
Isa Yildirim 3
Anca Maria Oprea 4
1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
2 Department of Mathematics, Hidaj Branch, Islamic Azad University, Hidaj, Iran
3 Department of Mathematics, Faculty of Science, Ataturk University, 25240 Erzurum, Turkey
4 Babe s-Bolyai University, Faculty of Mathematics and Computer Sciences, 400084 Cluj-Napoca, Romania
10.22075/ijnaa.2018.11820.1591
Abstract
In this paper, by using C-class functions, we will present a coupled fixed problem in b-metric space for the single-valued operators satisfying a generalized contraction condition. The first part of the paper is related to some fixed point theorems, the second part presents the uniqueness and existence of the solution of the coupled fixed point problem and in the third part, we discuss data dependence, well-posedness, Ulam-Hyers stability and limit shadowing property of the coupled fixed point set.
Keywords
Fixed point
ordered metric space
rational type contraction
coupled fixed point
data dependence
well-posedness
Ulam-Hyers stability
limit shadowing property
International Journal of Nonlinear Analysis and Applications
Volume 10, Issue 1
November 2019
Pages 77-98

  • Receive Date 03 February 2018
  • Revise Date 07 February 2019
  • Accept Date 24 March 2019

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