On Cauchy alpha and uniform alpha convergence

In this paper we introduced the notions of Cauchy alpha convergence and uniform alpha convergence for sequences of functions between metric spaces. Using these new concepts, we investigated properties between uniform convergence and alpha convergence and provided figures illustrating the relationships among these different types of convergence based on the structure of the functions and their domains. Finally, we established some Korovkin-type approximation theorems involving these new concepts.