(m1,m2)-Convexity and Some New Hermite-Hadamard Type Inequalities

In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-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.

(m1,m2)-Convexity and Some New Hermite-Hadamard Type Inequalities Keywords:

(m1 , m2)-Convex function , Hölder and Hölder-İşcan integral inequalities , power-mean and improwed power-mean integral inequalities , Hermite-Hadamard inequality