T-Partial G-Metric Spaces and an Application in Dynamic Programming

This paper introduces the new category of metrics termed T-partial G-metrics (X,J). The related topology satisfies the T2-separation axiom. We establish fixed-point theorems without requiring the compactness of X or the symmetry of J. These results generalize many existing theorems in the writings. In addition, we present an application in dynamic programming to demonstrate the practical relevance of our theoretical findings.