an application of fixed point theorems to dynamic programming in a generalized distance space

This study introduces a novel concept of a three-variable distance space, which extends several existing metric structures, including s-metric space, sb-metric, sθ-metric space, and sp-metric space. various topological properties of these spaces are examined. a fixed point theorem for generalized weak contraction mappings in this framework is established, accompanied by several related corollaries. to validate the space and the derived fixed-point theorem, illustrative examples are provided. finally, the fixed point theorem is applied to analyze the solution of a functional equation arising in dynamic programming.