Vol. 69, No. 3, pp. 214–225 (2017)

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Coupled fixed points for mappings on a b-metric space with a graph

A. K. Mirmostafaee

Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Iran E-mail: mirmostafaei@ferdowsi.um.ac.ir

Abstract: In this paper, we will develop a new method to study coupled fixed points of a mapping T:X×XX, where (X,d) is a special class of b-metric spaces endowed with a graph. We will prove some general fixed point theorems which enable us to extend some old results in fixed point theory. Moreover, we will extend Edelstein’s fixed point theorem for two variable mappings in ε-chainable b-metric spaces.

Keywords: Coupled fixed point; connected graph; Picard operator; b-metric space.

Classification (MSC2000): 47H10; 54M15, 54C10

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Electronic fulltext finalized on: 20 Jun 2017. This page was last modified: 7 Jul 2017.

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