COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN COMPLETE METRIC SPACES
By
A. K. Goyal and Gaurav Kumar Garg
Department of Mathematics M. S. J. Government Postgraduate College, Bharatpur, Rajasthan, India-321001
Email: akgbpr67@gmail.com, garg.gaurav770@gmail.com
(Received: June 01, 2023; In format: June 08, 2023; Revised: April 06, 2024; Accepted: April 12, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54124
Abstract
IJungck and Rhoades [13] introduced the notion of coincidentally commuting (weakly compatible) mappings, which is weaker than compatibility. Many interesting, fixed point theorems for weakly compatible maps satisfying contractive type conditions have been obtained by various authors. Goyal [5,6] prove some common fixed point theorems for six mappings involving rational contractive conditions by using notions of compatibility, weak compatibility and commutativity, in complete metric spaces. In this paper, we prove a common fixed point theorem for three pairs of weakly compatible mappings in complete metric spaces satisfying a rational inequality without any continuity requirement which generalize several previously known results due to Imdad and Ali [7], Goyal [5], Imdad-Khan [8], JeongRhoades [9] and others.
2020 Mathematical Sciences Classification: 54H25, 47H10
Keywords and Phrases: Complete metric spaces, fixed points, compatible mapping, weak compatible mapping.