Hermite-Hadamard type inequalities for n-times differentiable and geometrically quasi-convex functions

Jun Zhang; Feng Qi; Gao-Chao Xu; Zhi-Li Pei

doi:10.1186/s40064-016-2083-y

Hermite-Hadamard type inequalities for n-times differentiable and geometrically quasi-convex functions

Springerplus. 2016 Apr 26:5:524. doi: 10.1186/s40064-016-2083-y. eCollection 2016.

Authors

Jun Zhang¹, Feng Qi², Gao-Chao Xu³, Zhi-Li Pei⁴

Affiliations

¹ College of Computer Science and Technology, Jilin University, 130012 Changchun City, Jilin Province China ; College of Computer Science and Technology, Inner Mongolia University for Nationalities, 028043 Tongliao City, Inner Mongolia Autonomous Region China.
² Department of Mathematics, School of Science, Tianjin Polytechnic University, 300387 Tianjin City, China ; Institute of Mathematics, Henan Polytechnic University, 454010 Jiaozuo City, Henan Province China.
³ College of Computer Science and Technology, Jilin University, 130012 Changchun City, Jilin Province China.
⁴ College of Computer Science and Technology, Inner Mongolia University for Nationalities, 028043 Tongliao City, Inner Mongolia Autonomous Region China.

Abstract

By Hölder's integral inequality, the authors establish some Hermite-Hadamard type integral inequalities for n-times differentiable and geometrically quasi-convex functions.

Keywords: Hermite–Hadamard type inequality; Hölder integral inequality; geometrically quasi-convex function.