Solvability of Functional Equations’ Classes Arising in Dynamic Programming Using Fixed-Point Technique

This paper is devoted to the existence, uniqueness, and iterative approximation of solutions for the classes of functional equations arising in dynamic programming of multistage decision processes. The findings presented here extend and integrate several results from the existing literature. Illustrative examples are also provided to emphasize the significance of the main results. The approach is based on fixed point techniques applied in suitable function spaces. Furthermore, our results unify a variety of known theorems within a broader and more flexible framework.