A Note on Statistical Continuity of Functions

Abstract

In the present paper, we first recall the notion of statistical convergence of double sequences defined on topological spaces and reduced equivalent to the definition, along with some of its basic properties. Later, we define the concept of statistically continuous as a general case of the continuous function using the statistical convergence of double sequences. We define strong and weak statistically continuous functions as final definitions that arise as a direct consequence of statistically continuous functions. In the rest of the paper, we analyze the implications between the given definitions and investigate additional conditions for equality.