New Type of Strongly Continuous Functions in Topological Spaces via δ-β-Open Sets

Abstract

In this paper we introduce and investigate a new class of strong continuous functions called strongly θ-δ-β-continuous functions by using two new strong forms of δ-β-open sets called δ-β-regular sets and δ-β_θ-open sets. This class is a generalization of both strongly θ-e-continuous functions and strongly θ-β-continuous functions. Severalnew characterizations and fundamental properties concerning strongly θ-δ-β-continuous functions are obtained. Furthermore, the relationships between strongly θ-δ-β-continuous functions and other well-known types of strong continuity are also discussed.