A fixed point theorem in T-partial b-metric spaces and an application in dynamic programming

Here, a fixed point theorem is proved in a new class of spaces called [Formula: see text]-partial [Formula: see text]-metric spaces without using the compactness. This class of spaces is a new generalization of [Formula: see text]-metric spaces such that the generated topology is a Hausdorff topology. Moreover, an application in dynamic programming is given to illustrate the usability of the obtained results.