A New Common Fixed-Point Theorem for Two Pairs of Mappings in Parametric Metric Space
Anil Bakhru *
Department of Mathematics, Sardar Vallabhbhai Polytechnic College, College of University of Technology of Madhya Pradesh, Bhopal, 462002, India.
Manoj Ughade
Department of Post Graduate Studies and Research in Mathematics, Jaywanti Haksar Government Post Graduate College, College of Chhindawara University, Betul, 460001, India.
Richa Gupta
Department of Engineering Mathematics and Research Center, Sarvepalli Radhakrishanan University, Bhopal, 462026, India.
*Author to whom correspondence should be addressed.
Abstract
Our aim of this paper is to prove a new general common fixed point theorem for two pair of mappings under a different set of conditions using the idea of weakly compatible mappings satisfying a general class of contractions defined by an implicit relation in the frame work of parametric metric space, which unify, extend and generalize most of the existing relevant common fixed point theorems from the literature. Some related results and illustrative an example to highlight the realized improvements is also furnished.
Keywords: Parametric metric space, common fixed point; implicit relation, weakly compatible mappings, contractions.