ON CERTAIN CLASSES OF GENERALIZED CONVEX FUNCTIONS WITH APPLICATIONS, I

Abstract

The aim of this series of papers is to introduce certain new concepts of generalized convex functions with applications. The first part contains results related to the h-invex functions first introduced by the author in 1988. Here are studied also h-cvazi-invexity and generalized h-pseudo-invexity with connections to well known classes of functions as subadditive or Jensen-convex functions. The second part treats the so- called A-convex functions, due to the author. Finally the part III, on L- invex functions, leads to a generalization of the Banach-Steinhaus theorem of condenzation of singularities.