An application for dynamic programming via fixed point theorem using rational type

Abstract

In this study, we introduce and investigate the concept of generalized multivalued rational type $F$-contractions on spherically complete ultrametric spaces. Building upon the existing framework of fixed point theory, we establish novel fixed point theorems for such mappings and provide several corollaries that extend and unify known results in the literature. To highlight the applicability of our findings, we present an illustrative example that demonstrates the validity of the proposed approach. Furthermore, we explore an application to dynamic programming by formulating functional equations whose solutions can be obtained through the developed fixed point techniques. The results not only broaden the scope of contraction principles in non-Archimedean settings but also emphasize the utility of ultrametric structures in optimization and computational mathematics.