(m۱,m۲)-Convexity and Some New Hermite-Hadamard Type Inequalities

In this manuscript, a new class of extended (m۱,m۲)-convex and concave functions is introduced. After some properties of (m۱,m۲)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than with Hölder integral inequality and improwed power-mean inequality gives a better approach than with power-mean inequality.

Keywords:

(m۱ , m۲)-Convex function , Hölder and Hölder-İşcan integral inequalities , power-mean and improwed power-mean integral inequalities , Hermite-Hadamard inequality