Harmonic beta-convex functions involving hypergeometric functions

摘要

We introduce and study a new class harmonic convex functions, which is called harmonic beta-convex functions. This new class includes several new and previously known classes of harmonic convex functions as special cases. We obtain some new integral inequalities involving hypergeometric functions. Some special cases are also discussed. Results obtained in this paper continue to hold for these cases. Ideas and techniques of this paper may stimulate further research.