Unique Common Tripled Fixed Point for Three Mappings in <img src=image/13424616_01.gif> Spaces

Abstract

It has been a century since the Banach fixed point theorem was established, and because of this, the result is the progenitor in some ways. This seems essential to revisit fixed point theorems in specific and in light of most of those. Those are numerous and prevalent in mathematics, as we will demonstrate. Fixed point theorems can be noticed in advanced mathematics, economics, micro-structures, geometry, dynamics, computational mathematics, and differential equations. <img src=image/13424616_03.gif> space is to broaden and extrapolate the paradigm of the concept of metric space. The characteristic of a <img src=image/13424616_03.gif> space, in essence, is to comprehend the topological features of three points rather than two points via the perimeter of a triangle, where the metric indicates the distance between two points. The domain of <img src=image/13424616_02.gif> space is significantly larger than that of the class of <img src=image/13424616_03.gif> space. Hence we utilised this generalized space in order to obtain common tripled fixed point for three mappings using rational type contractions in the setting of <img src=image/13424616_02.gif> spaces. Recently, Khomadram et al have developed coupled fixed point theorems in <img src=image/13424616_02.gif> spaces via rational type contractions. The main aim of our paper is to broaden and extrapolate the paradigm of Khomadram's results into tripled fixed point theorems. Therefore, examples are offered to support our findings.