On a generalized Krasnoselskii fixed point theorem

Abstract

This study concerns a Krasnoselskii-type fixed point theorem for the sum of two operators A,BA,B in a Banach space EE, where BB is a Reich-type contractive mapping and AA is a k-set contractive mapping. We introduce a class of operators θ:X×X→[1,+∞)\theta :X\times X\to \left[1,+\infty ) satisfying some axioms and use it as a new metric to prove a fixed point theorem in the spirit of Azam et al. [Reich-Krasnoselskii-type fixed point results with applications in integral equations, J. Inequal. Appl. 2023 (2023), 131].

Keywords

• reich contraction
• darbo k-set contraction
• krasnoselskii fixed point theorem
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