Several integral inequalities for (<em>α</em>, <em>s</em>,<em>m</em>)-convex functions

Abstract

In this paper, we establish several new integral inequalities for (α, s,m)-convex functions. We recapture the Hermite-Hadamard inequality as a particular case. In order to obtain our results, we use classical inequalities such as Hölder inequality, Hölder-Işcan inequality and Power mean inequality. We formulate several bounds involving special functions like classical Euler-Gamma, Beta and PsiGamma functions. We also give some applications.

Keywords

• convex function
• (<i>α</i>
• <i>s</i>
• <i>m</i>)-convex function
• hermite-hadamard inequality
• riemann-liouville fractional integrals
• hölder’s inequality
• power mean inequality
• psi-gamma functions