Common fixed point of mappings satisfying rational inequalities in ordered complex valued generalized metric spaces

Abstract

Azam et al. (Numer Funct Anal Optim, 32(3):243-253, 2011) introduced a notion of complex valued metric space and obtained common fixed point result for mappings in such spaces. In this paper, introducing the concept of complex valued generalized metric spaces, some fixed and common fixed point results are obtained. As an application, periodic point property of common fixed point problem for two rational type contractive mappings involved therein is established. Keywords Weakly increasing map • Common fixed point • Periodic point • Complex valued generalized metric spaces • Partially ordered set • BA-cone metric space

Common Coupled Fixed Point of Mappings Satisfying Rational Inequalities in Ordered Complex Valued Generalized Metric Spaces

“…In this paper, we extend the result of M. Abbas et al [18] fixed point to coupled fixed point in complex valued generalized metric space.…”

Fixed Point Sets of Multivalued Contractions and Stability Analysis

“…Rational terms were used in problems of fixed point theory in a good number of papers. Such uses were initiated by Dass et al [27] and were subsequently made in several works on fixed point theory of which some recent references are [12], [28], [29]- [32].…”

COMMON COUPLED FIXED POINTS FOR FOUR MAPS USING alpha-ADMISSIBLE FUNCTIONS IN COMPLEX VALUED b- METRIC SPACES

“…Azam et al [1] introduced the notion of complex valued metric space which is a generalization of the classical metric space and obtained sufficent conditions for the existence of common fixed points of a pair of mappings satisfying a rational contractive condition.Later several authors proved fixed and common fixed point theorems in complex valued metric spaces, for example, refer [3,4,6,8,11,12,14,16,20,21,28]. Recently some authors,for example [7,13,17,22,24,25,26], obtained coupled and common coupled fixed point point theorems for a pair of mappings in complex valued metric spaces.…”