Using Helping Function with Specific Conditions to Develop Some Results of the Literature

Abstract

In this study, we establish existence and uniqueness results for fixed points in complete metric spaces using a helping function approach. The proposed framework generalizes and unifies several well-known fixed point theorems, including those of Banach, Kannan, and Chatterjea. Our results extend the current literature by providing broader conditions under which common fixed points can be guaranteed, thus contributing to the ongoing development of fixed point theory in metric spaces.