Approximating common fixed points under generalized rational contractions in 2-Banach spaces with applications

Abstract

In this manuscript, the existence and uniqueness of common fixed points of a family of self-mappings under more generalized rational contractive conditions in 2-Banach spaces are obtained with an illustrative example. Then the common fixed points are approximated by means of Krasnoselskii, Mann and Picard type iteration schemes. Later, an application to well-posedness of the common fixed point problem is provided. The obtained results generalize and improve many well-known results in the literature.