Several generalizations of Is*g -Continuous Functions in Ideal Topological Spaces

Abstract

Khan and Noiri( Khan M. and Noiri T., On Is*g -continuous functions in the Ideal Topological spaces, Eur. J. Pure Appl. Math., 4(3)(2011), 237 – 243.) have initiated the notion of Is*g -continuous functions in ideal Topological spaces. In addition to this, they have also defined the strong and weak versions of Is*g -continuous functions along with their mutual relationships and studied certain properties of these functions. By considering the definition of β-open sets, the authors have proposed the generalization of Is*g -continuous functions viz. Is*g -β-continuous functions in the present paper. Moreover, the generalization of weak I-continuous functions and weakly Is*g -continuous functions have been defined in the context of β-open and regular open sets. The relationships amongst these continuities have been also established and the generalization has been justified by several illustrative examples.