Tripled fixed point theorems for non-compatible self-maps in generalized metric spaces

Abstract

In this paper, we develop a new tripled fixed point theorem for three interacting self-maps by using the notions of R-weak commutativity of type and non-compatibility in generalized metric spaces. We can establish our results without assuming the completeness of the underlying generalized metric space or the continuity of the mappings, thereby removing hypotheses that commonly restrict the applicability of existing tripled fixed point results. To support our findings, a detailed example is provided that illustrates the novelty, validity, and mathematical relevance of the proposed theorem.