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

Subject Areas : International Journal of Mathematical Modelling & Computations

Huriye Kadakal ¹

1 - Ministry of Education, Hamdi Bozbag Anatolian High School, Giresun, Turkey

Received: 2019-07-30 Accepted : 2019-11-10 Published : 2019-12-01

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

Abstract :

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.