  The main purpose of this study is to introduce and study two new classes of
continuity called eR-continuous functions and weakly eR-continuous functions
via e-regular sets. Both of the forms of continuous functions we have described
are stronger than the weakly e-continuity. Furthermore, we obtain various
characterizations of weakly eR-continuous functions. In addition, we examine
not only the relations of these functions with some other forms of existing
continuous functions, but also some of their fundamental properties.
