Applications of de Rham theorem in approximate midconvexity

Abstract

Let X be a normed space, V be an open convex subset of X and let be a given function. A function is called -midconvex if By the result of Tabor and Tabor, we know that under respective conditions on , if f is -midconvex and locally bounded above at a point then there exists a continuous function such that In this paper we determine the smallest function satisfying the above inequality. The required conditions on are such that the functions , satisfy them. As the main tool we use de Rham theorem.