On the notion of (γ, s)-continuous functions

In 2002, Noiri and Jafari studied the notion of (θ, s)-continuous functions due to Thompson [Proc. Amer. Math. Soc. 60 (1976) 335-338]. In this paper, a new generalization of (θ, s)-continuity which is called (γ, s)-continuity is introduced and studied. Furthermore, characterizations, basic properties, preservation theorems of (γ, s)-continuous functions and relationships between (γ, s)-continuous functions and the other types of functions are investigated and obtained.