Hermite-Hadamard Integral Inequalities Of Some Convex Functions And Their Applications

There have been many studies on Hermite-Hadamard type integral inequalities for convex functions,and a number of fruitful results have come out of these studies.Many achievements have been made on integer convex functions.In recent years,more and more scholars have generalized integral inequality of integer order to fractional order.Combining with the interval analysis theory,some scholars begin to study the Hermite-Hadamard integral inequality of interval-valued convex functions,which make the applications of integral inequality more extensive.In this paper,inspired by previous studies,we establish a new fractional Hermite-Hadamard integral inequality on s-(?,m)-convex functions by using related scaling and contracting techniques,and give a new estimate and the application of the re-sults.This paper also defines of two new classes of(h1,h2)-convex and harmonical(h1,h2)-convex interval-valued function,studies integral inequalities of the integer order on these two new classes of interval convex functions,and extends it to the fractional order,which enriches the research topic of the integral inequalities of the Hermite-Hadamard,and plays an important role in the research of related fields.According to the content,this paper is divided into the following four chapters:Chapter 1 Preference-we introduce the research background for this paper.Chapter 2 We study some fractional Hermite-Hadamard type integral inequalities with s-(?,m)-convex functions:??Chapter 3 We study Hermite-Hadamard type inequalities for harmonical(h1,h2)-convex interval-valued functions:??Chapter 4 we consider some Hermite-Hadamard type inequalities for two class of interval-valued convex functions:...