Fixed Point Theorems in Elliptic-Valued Suprametric Spaces and Their Applications

The purpose of this article is to introduce the concept of elliptic-valued suprametric spaces and to establish some common fixed point theorems within this newly proposed framework. The development of elliptic-valued suprametric spaces, along with the main results presented here, is illustrated through non-trivial examples. As applications, we employ our fixed point results to study the nonlinear Volterra integral equation of the second kind, demonstrating the existence and uniqueness of solutions under suitable conditions. In particular, we highlight the role of such equations in age-structured population models, where they serve as powerful tools for describing hereditary effects, density-dependent interactions, and delayed responses in population dynamics. This connection bridges the abstract theory with applied contexts in mathematical biology, ecology, and epidemiology, emphasizing the relevance of elliptic-valued suprametric structures in both theoretical analysis and real-world applications. Furthermore, we derive corresponding fixed point results in elliptic-valued suprametric spaces, complex-valued suprametric spaces, elliptic-valued metric spaces, and complex-valued metric spaces as corollaries of our main findings.