Rizwan Anjum, Mujahid Abbas, and Ravi P. Agarwal
Fixed Points of Enriched Condensing Operators in Ordered Banach Spaces
Dynamic Systems and Applications 32 (2023) 314-331

https://doi.org/10.46719/dsa2023.32.17

ABSTRACT.
The aim of this paper is to obtain common fixed point results for a pair of condensing and weakly isotone self-mappings on ordered Banach spaces by the technique of enrichment. We present a new generalization of Darbo fixed point theorem in the setting of Banach spaces. These results unify and complement various known results in the existing literature on common fixed point theory. Some examples are given to support the concepts and results presented in this paper. Existence of the solution of two nonlinear differential equations is proved as an application of the result presented herein.

AMS (MOS) Subject Classification. 47H09, 47H10, 34A12.

Key Words and Phrases. Fixed point, Condensing operators, weakly isotone mappings, enriched contraction, ordered Banach space