Fixed point theory in elliptic-valued metric spaces: applications to Fredholm integral equations and climate change analysis

The aim of this research article was to explore the framework of elliptic-valued metric spaces and establish novel common fixed point theorems for a wide range of generalized contraction mappings. Our findings provide a significant extension and unification of existing fixed point results, offering more refined mathematical tools for analyzing nonlinear problems in abstract spaces. To illustrate the effectiveness of our theorems, we present a concrete example that underscores the originality of our approach. Additionally, we highlight the practical significance of our main result by applying it to solve a nonlinear Fredholm integral equation of the second kind, which plays a crucial role in climate modeling. This equation is essential for understanding temperature distribution dynamics and feedback mechanisms within Earth's energy balance system. By bridging theoretical developments in metric space theory with real-world climate applications, this study contributes to both mathematical research and environmental science.