On Hadamard inequalities for refined convex functions via strictly monotone functions

In this paper, we define refined $(\alpha ,h-m)$-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, $(\alpha ,m)$-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.