An Opial-type integral inequality and exponentially convex functions

Abstract

In this paper a certain class of convex functions in an Opial-type integral inequality is considered. Cauchy type mean value theorems are proved and used in studying Stolarsky type means defined by the observed integral inequality. Also, a method of producing n-exponentially convex and exponentially convex functions is applied. Some new Opial-type inequalities are given for different types of fractional integrals and fractional derivatives as applications.