Advancing Fixed Point Theory in Elliptic-Valued Suprametric Spaces

The purpose of this research article is to establish common fixed point results for generalized contractions defined with control functions in the framework of elliptic-valued suprametric spaces. By utilizing the structure and properties of these spaces, we develop new fixed point results that extend and unify several known theorems in the literature. The theoretical findings are illustrated through a series of non-trivial examples, demonstrating the applicability and robustness of the proposed approach. As a concrete application, we employ the established fixed point theorems to analyze the existence and uniqueness of solutions for nonlinear Volterra integral equations of the second kind. Furthermore, the results obtained herein naturally encompass a wide range of fixed point theorems previously reported in the literature as direct corollaries, emphasizing the broad applicability and flexibility of the proposed framework.