Hermite--Hadamard type inequalities for (\(\alpha,m\))-HA and strongly (\(\alpha,m\))-HA convex functions

Volume 10, Issue 1, pp 205--214 http://dx.doi.org/10.22436/jnsa.010.01.20

Publication Date: January 27, 2017 Submission Date: October 23, 2016

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Authors

Chun-Ying He - College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China. Yan Wang - College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China. Bo-Yan Xi - College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China. Feng Qi - Department of Mathematics, College of Science, , Tianjin Polytechnic University, Tianjin City, 300160, China. - Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China.

Abstract

In the paper, the authors define the concepts of (\(\alpha,m\))-harmonic-arithmetically convex functions and strongly (\(\alpha,m\))- harmonic-arithmetically convex functions, establish a new integral identity, and present some new Hermite–Hadamard type inequalities for (\(\alpha,m\))-harmonic-arithmetically convex functions and strongly (\(\alpha,m\))-harmonic-arithmetically convex functions.

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Keywords

• Strongly (\(\alpha،m\))-harmonic-arithmetically convex function
• (\(\alpha،m\))-harmonic-arithmetically convex function
• integral identity
• Hermite–Hadamard type integral inequality.

MSC

•  26A51
•  26D15
•  41A55

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