On almost e-ℐ-continuous functions

Abstract

Abstract This work is concerned with a new class of functions called almost e e - ℐ {\mathcal{ {\mathcal I} }} -continuous functions containing the class of almost e e -continuous functions. This notion is stronger than almost δ β ℐ \delta {\beta }_{{\mathcal{ {\mathcal I} }}} -continuous functions and is weaker than both almost e e -continuous functions and e e - ℐ {\mathcal{ {\mathcal I} }} -continuous functions. Relationships between this new class and other classes of functions are investigated and some characterizations of this new class of functions are studied.