A Common Coupled Fixed Point Theorem in Complex Valued Metric Space

Abstract

The aim of this paper is to establish a unique common coupled fixed point theorem for two mappings satisfying a rational inequality in complex valued metric space.

Rational Type Contraction in b-Metric Spaces and Common Coupled Fixed Point Theorems

“…In this work, we found two main results, which are given in Theorem 3.1 and Theorem 3.2. with Corollaries 3.1 and 3.2, respectively. The present Theorem 3.1 and Theorem 3.2 extend, modify, and generalize the results of the Theorems 2.2 and 2.3 of the literature [26].…”

“…The aim of this article is to construct and obtain new results on common coupled fixed points for a pair of mappings satisfying rational type contraction. The found results are extended and change various results from the existing literature of [26].…”

Fixed point theorems based on well-posedness and periodic point property in ordered bicomplex valued metric spaces

“…In 2011, Azam et al [2] introduced the notion of complex valued metric spaces and established some fixed point results for a pair of mappings for contraction condition satisfying a rational expression. Since then several authors studied the existence and uniqueness of fixed points of self-mappings and established fixed point results on complex valued metric spaces (see [1], [3], [12], [14], [16]).…”

Common Coupled Fixed Point Results for Generalized Rational Type Contractions in Complex Valued Metric Spaces

“…The concept of coupled fixed point was first introduced by Bhaskar and Laxikantham [10] in 2006.Recently some researchers prove some coupled fixed point theorems in complex valued metric space in [11], [12]. In [1],Marwan Amin Kutbi et al,gave a common coupled fixed point results for generalized contraction in complex valued metric space and proved following theorem.…”