on tβ-contractive mappings: fixed point results with an application

We introduce the concept of tβ-contractive mappings in the framework of bounded metric spaces and prove the existence of a fixed point for such mappings without using neither the compactness nor the uniform convexity of the space. furthermore, a fixed point theorem for tβ-weakly contractive maps has been given. we point out that, these results generalize and improve many previous works in the literature. ultimately, one of our theoretical results has been implicated to study the existence of the solution to a class of functional equations arising in dynamic programming under new weak conditions.