# Hermite-Hadamard type integral inequalities for geometric-arithmetically $(s,m)$ convex functions

Volume 15, Issue 4, pp 253--266
Publication Date: May 27, 2022 Submission Date: January 27, 2022 Revision Date: February 28, 2022 Accteptance Date: March 10, 2022
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### Authors

X.-Li. Cheng - Department of Mathematics, Jilin Normal University, Siping, 136000, China. H.-W. Zuo - School of Mathematical Sciences, Capital Normal University, Beijing, 10048, China. Z.-Q. Hua - College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, 028043, China.

### Abstract

In this paper, we introduce a definition of geometric-arithmetically $(s,m)$ convex function and give some new inequalities of Hermite-Hadamard type for the geometric-arithmetically $(s,m)$ convex function. Finally, we discuss applications of these inequalities to special means.

### Share and Cite

##### ISRP Style

X.-Li. Cheng, H.-W. Zuo, Z.-Q. Hua, Hermite-Hadamard type integral inequalities for geometric-arithmetically $(s,m)$ convex functions, Journal of Nonlinear Sciences and Applications, 15 (2022), no. 4, 253--266

##### AMA Style

Cheng X.-Li., Zuo H.-W., Hua Z.-Q., Hermite-Hadamard type integral inequalities for geometric-arithmetically $(s,m)$ convex functions. J. Nonlinear Sci. Appl. (2022); 15(4):253--266

##### Chicago/Turabian Style

Cheng, X.-Li., Zuo, H.-W., Hua, Z.-Q.. "Hermite-Hadamard type integral inequalities for geometric-arithmetically $(s,m)$ convex functions." Journal of Nonlinear Sciences and Applications, 15, no. 4 (2022): 253--266

### Keywords

• Integral inequality
• geometric-arithmetically $(s,m)$ convex function
• Holder inequality

•  26D15
•  26A51

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