Abstract: This paper establishes a common fixed point theorem for six weakly compatible mappings in complete <i>M∗</i>-metric spaces, generalizing previous results in D∗-metric and related spaces. We introduce enhanced versions of fixed point theorems under weak compatibility conditions, leveraging a continuous and increasing function ϕ to derive contraction inequalities. Our main theorem demonstrates the existence and uniqueness of a common fixed point, supported by illustrative examples. Additionally, we extend these findings to families of mappings, ensuring broader applicability. The results contribute to fixed point theory in generalized metric spaces, offering potential applications in nonlinear analysis and differential equations. This paper builds upon and refines existing literature, providing a foundation for further research in metric space fixed point theory.

Keywords: D∗−metric spaces, M∗−metric spaces, M∗−metric contractive mapping, complete M∗− metric space, Weakly compatible mappings, Common fixed point theorem

Pages: 137-146