Results on fixed points in b-metric space by altering distance functions

N Seshagiri Rao; Ahmad Aloqaily; Nabil Mlaiki

doi:10.1016/j.heliyon.2024.e33962

Results on fixed points in b-metric space by altering distance functions

Heliyon. 2024 Jul 5;10(14):e33962. doi: 10.1016/j.heliyon.2024.e33962. eCollection 2024 Jul 30.

Authors

N Seshagiri Rao¹, Ahmad Aloqaily^{2

3}, Nabil Mlaiki²

Affiliations

¹ Department of Mathematics & Statistics, School of Applied Science & Humanities, Vignan's Foundation for Science, Technology & Research, Vadlamudi-522213, Guntur, Andhra Pradesh State, India.
² Department of Mathematics and Sciences, Prince Sultan University, Riyadh-11586, Saudi Arabia.
³ School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney-2150, Australia.

Abstract

We discuss the existence of a fixed point for a self mapping and its uniqueness satisfying $(\dot{ϕ}, \dot{η})$ -generalized contractive condition including altering distance functions of rational terms in an ordered b-metric space. It is also discussed whether the two self-maps under the same contraction condition can be coincident and coupled coincident. The results are backed up by a dearth of numerical examples and application to nonlinear quadratic integral equation.

Keywords: ( ϕ ˙ , η ˙ ) -weak contraction; 47H10; 54H25; Coincidence point; Compatible mappings; Fixed point; Ordered metric spaces.