Affirmative Fixed Point Results for Four Weakly Compatible Self-maps in a Complete Sb-metric Space

Abstract

In this article, an attempt is made to establish certain fixed point theorems for four pairwise self-maps that are weakly compatible in a complete S_b-metric space. Four self-maps in a complete S_b-metric space are considered, and a contractive condition is applied together with the weak compatibility of pairs of mappings. Some pre-existing results that hold in ordinary metric spaces are examined and validated in the setting of a complete S_b-metric space. By applying a contractive condition along with the weak compatibility of pairs of mappings, the existence of a fixed point is established, and its uniqueness is subsequently proved. Two fixed point theorems corresponding to two different contractive conditions are proved. In each case, a corollary is obtained by restricting the results to two self-maps.