On weakly e-continuous functions

The main goal of this paper is to introduce and look into some of the fundamental properties of weakly e-continuous functions defined via e-open sets introduced by E. Ekici (On e-open sets, DP*-sets and DP?*- sets and decompositions of continuity, Arab. J. Sci. Eng. 33 (2A), 269-281, 2008). Some characterizations and several properties concerning weakly e-continuous functions are obtained. The concept of weak e-continuity is weaker than both the weak continuity introduced by N. Levine (A decomposition of continuity in topological spaces, Amer. Math. Monthly 68, 44-46, 1961) and the e-continuity introduced by Ekici, but stronger than weak ß-continuity introduced by Popa and Noiri (Weakly ß-continuous functions, An. Univ. Timis. Ser. Mat.-Inform. 32(2), 83-92, 1994). In order to investigate some different properties we introduce the concept of e-strongly closed graphs and also investigate relationships between weak e-continuity and separation axioms, and e-strongly closed graphs and covering properties.