Approximation of common fixed points in 2-Banach spaces with applications

Abstract

The purpose of this paper is to establish the existence and uniqueness of common fixed points of a family of self-mappings satisfying generalized rational contractive condition in 2-Banach spaces. An example is included to justify our results. We approximate the common fixed point by Mann and Picard type iteration schemes. Further, an application to well-posedness of the common fixed point problem is given. The presented results generalize many known results on 2-Banach spaces.

Keywords

• common fixed point
• Mann iteration
• Picard iteration
• well-posedness
• 2-Banach space