Approximately two-dimensional harmonic \((p_{1},h_{1})\) - \((p_{2},h_{2})\) -convex functions and related integral inequalities

Journal of inequalities and applications

article

Saad Ihsan Butt¹  Artion Kashuri²  Muhammad Nadeem¹  Adnan Aslam³  Wei Gao⁴ 

[1] COMSATS University Islamabad;Department of Mathematics, Faculty of Technical Science, University Ismail Qemali;Department of Natural Sciences and Humanities, University of Engineering and Technology;School of Information Science and Technology, Yunnan Normal University

关键词: Hermite–Hadamard inequality;    Hölder inequality;    Convexity;   

DOI  :  10.1186/s13660-020-02495-6

学科分类：电力

来源: SpringerOpen

【 摘 要 】

The aim of this study is to introduce the notion of two-dimensional approximately harmonic $(p_{1},h_{1})$ - $(p_{2},h_{2})$ -convex functions. We show that the new class covers many new and known extensions of harmonic convex functions. We formulate several new refinements of Hermite–Hadamard like inequalities involving two-dimensional approximately harmonic $(p_{1},h_{1})$ - $(p_{2},h_{2})$ -convex functions. We discuss in detail the special cases that can be deduced from the main results of the paper.

【 授权许可】

CC BY