The concept of induced fuzzy topological space, introduced by Weiss [J. Math. Anal. Appl. 50(1975), 142-150], was defined with the notion of a lower semi-continuous function. The aim of this paper is to introduce and study the concepts of induced fuzzy supra-topological spaces and s-lower β-continuous functions. s-Lower β-continuous functions turn out to be the natural tool for studying the ind...

In this paper, we give twoweak conditions for a lower semi-continuous function on the n-dimensional Euclidean space Rn to be a convex function. We also present some results for convex functions, strictly convex functions, and quasi-convex functions.