Application of fixed point result to the boundary value problem using the $ M $-type generalized contraction condition for best proximity point considerations

This paper serves a dual purpose: to introduce a contraction condition and to demonstrate its application. We established a new framework for obtaining best proximity points in complete metric spaces, extending and generalizing several existing fixed point theorems. From this foundational result, multiple corollaries were derived, providing broader applicability in various mathematical settings. To validate the theoretical development, we applied our results to boundary value problems and dynamic market equilibrium models, illustrating both the mathematical robustness and real-world relevance of the proposed method.