On Cauchy Alpha and Uniform Alpha Convergence

Abstract

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