SOME INTEGRAL INEQUALITIES OF HERMITE-HADAMARD TYPE FOR DIFFERENTIABLE (s; m)-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS

SOME INTEGRAL INEQUALITIES OF HERMITE-HADAMARD TYPE FOR DIFFERENTIABLE (s; m)-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS

B. Bayraktar

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Abstract

In this paper, we present new inequalities connected with fractional integrals for twice dierentiable functions derivatives which are (s;m)- convex functions. To obtain this, integral inequalities were used classical inequalities as Holder inequalitiy and power mean inequality.This results are related to the well-known integral inequality of the Hermite-Hadamard type. Also some applications to special means are provided.

Keywords

convex function,(s;m)-convex, Hermite{Hadamard inequalitiy, Riemann{ Liouville fractional integral, power mean inequalitiy, Holder inequality.