Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations

Abstract

We present some new common fixed point theorems for a pair of nonlinear mappings defined on an ordered Banach space. Our results extend several earlier works. An application is given to show the usefulness and the applicability of the obtained results.

Common fixed point results of generalized almost rational contraction mappings with an application

“…Due to its applications in mathematics and other related disciplines, Banach contraction principle has been generalized in many directions. Extensions of Banach contraction principle have been obtained either by generalizing the domain of the mapping or by extending the contractive condition on the mappings (see, [1,2,3,4,5,6,7,10,11,13,14,15,16,18,19,22,23,24,26,27,28,29,30,31,32,34,35] and references therein).…”

Best Proximity Point Results in Non-Archimedean Modular Metric Space

“…The existence of best proximity points in partially-ordered metric spaces has been investigated in recent years by many authors (see, [24] and the references therein). In this section, we introduce a new notion of Suzuki-type ordered (β, θ, γ)-contractive mapping and investigate the existence of the best Author Contributions: The authors equally contribute in the preparation of this manuscript.…”

Coupled coincidence point results for a generalized compatible pair with applications

“…Box 80203, Jeddah, 21589, Saudi Arabia. 2 Department of Mathematics and Applied Mathematics, University of Pretoria, Lynwood Road, Pretoria, 002, South Africa. 3 Department of Mathematics, COMSATS Institute of Information Technology, Chack Shahzad, Islamabad, 44000, Pakistan.…”