Type (K) Compatible Mappings and Common Fixed Points in Complete Cone S-metric Spaces

Objective: This research work is an attempt to explore common fixed points for four self-maps that are pairwise type ( ) compatible in a complete cone -metric space. Method: We have applied a contractive condition together with a weaker condition, compatible of type (K) to establish fixed points that are common for four self-maps. Findings: Some already existing results in the literature have been generalized, expanded upon, and new fixed point results have been obtained in cone S-metric spaces. To back up our conclusions, a suitable example is provided. Novelty: By adopting an appropriate contractive condition, we have proven the existence of a unique common fixed point for four maps in a cone -metric space, despite the weak compatible condition. MSC 2020: 47H10, 54H25. Keywords: Normal Cone, Partial Ordering, Cone S-metric Space, Compatible Mappings of Type (K), Common Fixed Point