Contra-e-Continuous Functions

In 2008, E. Ekici [13] introduced a new class of generalized open sets in a topological space called e-open sets. M. Ozkoc and G Aslim [26], in their recent paper (Bull. Korean Math. Soc. 47 (2010), No. 5, pp. 1025–1036), initiated two strong forms of e-open sets for the study of strongly-θ-e-continuous functions. J. Dontchev [8] introduced the notion of contra continuous functions. In this paper, by means of e-open sets, we introduce and investigate certain ramifications of contra continuous and allied functions, namely, contra-e-continuous, almost-e-continuous, almost weakly-e-continuous and almost contra-e-continuous functions along with their several properties, characterizations and mutual relationships. Further, we introduce new types of graphs, called e-closed, contra-e-closed and strongly contra-e-closed graphs via e-open sets. Several characterizations and properties of such notions are investigated.