Extended fixed point results for nonextensive mappings in convex metric spaces

This paper delves into establishing common fixed point results for asymptotically regular and nonexpansive-type mappings within convex metric spaces. It extends Gornicki’s contractive-type mapping theorems to include metric spaces with a convex structure, while building on Khan and Oyetubi’s work on common fixed points of asymptotically regular mappings satisfying the Reich-type contractive condition in complete metric spaces. By generalizing these results to convex metric spaces, the study introduces analogous findings for enriched Ciric-Reich-Rus-type contractions, contributing significantly to the advancement of fixed point theory in structured metric environments. The paper also demonstrates a common fixed point solution for pairs of compatible maps in convex metric spaces and presents a novel fixed point result for non-expansive type mappings in Banach spaces. Furthermore, an approximation result is achieved for quasi-nonexpansive mappings through the utilization of Ishikawa iterations in uniformly convex metric spaces. An additional feature of this study is the inclusion of graphs illustrating various convergence and dynamic behaviors, which provide valuable visual insights into system responses under differing conditions. The results are framed within the scope of the Banach Contraction Principle, enriching its applicability to broader classes of mappings and spaces.

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