Abstract
In this paper, we define a new axiom called gamma-s*-regularity. It is interesting to mention that this axiom is a generalization of the axiom of s-regularity [11] as well as semi-regularity [4]. We also introduce and investigate the notion of almost gamma-s-continuous functions. It will turn out that each of almost gamma-s-continuous functions [13] and almost gamma-s-continuous functions are independent notions.