Common Fixed Point Results of Asymptotically Regular Mappings in Generalized Metric Spaces with Application

Abstract

In this paper, we establish common fixed point results for two regular asymptotic mappings in b-metric spaces and strong b-metric spaces. Our main result deals with regular asymptotic contracting mappings of the Hardy-Rogers-Proinov-Górnicki type. We apply one of our new results to the solution of the Fredholm linear integral equation. We also obtain a common fixed point result for multivalued regular asymptotic mappings in a strong b-metric space, which is a modification and extension of the work of previous authors. Examples are given in support of the new concepts and results.