Some Common Fixed Point Theorems for Weakly Compatible Mappings in Rectangular S-Metric Spaces

Abstract

This paper explores the existence of common fixed points for weakly compatible mappings in the framework of rectangular S-metric spaces, a generalization of traditional S-metric spaces. By introducing suitable contractive conditions, we establish new common fixed point theorems that unify and extend various known results in the field of fixed point theory. These theorems provide broader applicability and deeper insights into the behaviour of such mappings under generalized metric conditions. The developed results not only contribute to the theoretical understanding but also enhance the scope of fixed point analysis in more generalized settings. To illustrate the validity and applicability of the main results, we provide several relevant examples. These examples serve to clarify the theoretical findings and demonstrate how the established theorems can be effectively applied in practice. Overall, the study offers a meaningful advancement in the general theory of fixed points within the context of rectangular S-metric spaces.