IMPROVEMENTS OF THE GIACCARDI AND THE PETROVIC INEQUALITY AND RELATED STOLARSKY TYPE MEANS

Abstract

Improvements of the Giaccardi and the Petrovi´c inequality are given. The notion of n􀀀exponentially convex functions is introduced. An elegant method of producing n􀀀exponentially convex and exponentially convex functions is applied using the Giaccardi and the Petrovi´c differences. Cauchy mean value theorems are proved and shown to be useful in studying Stolarskytype means defined by using the Giaccardi and the Petrovi´c differences.