On Hadamard inequalities for refined convex functions via strictly monotone functions

Abstract

In this paper, we define refined (α,h−m)-convex function with respect to a strictly monotone function. This function provides refinements of various well-known classes of functions for specific strictly monotone functions. By applying definition of this new function we prove the Hadamard inequalities for Riemann-Liouville fractional integrals. These inequalities give the refinements of fractional Hadamard inequalities for convex, (α,m)-convex, (h−m)-convex, (s,m)-convex, h-convex and many other related well-known classes of functions implicitly. Also, Hadamard type inequalities for k-fractional integrals are given.

Keywords

• convex function
• refined (α，h−m)-convex function
• monotone function
• hadamard inequality
• riemann-liouville fractional integrals