A variant of Jensen-type inequality and related results for harmonic convex functions

Imran Abbas Baloch; Aqeel Ahmad Mughal; Yu-Ming Chu; Absar Ul Haq; Manuel De La Sen; Imran Abbas Baloch; Aqeel Ahmad Mughal; Yu-Ming Chu; Absar Ul Haq; Manuel De La Sen

doi:10.3934/math.2020412

AIMS Mathematics

2020, Volume 5, Issue 6: 6404-6418. doi: 10.3934/math.2020412

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Research article

A variant of Jensen-type inequality and related results for harmonic convex functions

1.
Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan
2.
Higher Education Department, Government College for Boys Gulberg Lahore, Punjab, Pakistan
3.
Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan
4.
Department of Mathematics, Huzhou University, Huzhou, 313000, P. R. China
5.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China
6.
Department of Basic Sciences and Humanities, University of Engineering and Technology, Lahore (Narowal Campus), Pakistan
7.
Institute of Research and Development of Processors, University of the Basque, Country campus of Leioa (Bizkaia), 48940 Leioa, Spain

Received: 21 June 2020 Accepted: 03 August 2020 Published: 13 August 2020
MSC : 26D15, 26A51, 26D10, 26A15

In this article, we present a variant of discrete Jensen-type inequality for harmonic convex functions and establish a Jensen-type inequality for harmonic h-convex functions. Furthermore, we found a variant of Jensen-type inequality for harmonic h-convex functions.
- convex functions,
- harmonic convex functions,
- harmonic h-convex functions,
- Jensen-type inequality,
- discrete Hölder inequality,
- Hermite-Hadamard-type inequality
Citation: Imran Abbas Baloch, Aqeel Ahmad Mughal, Yu-Ming Chu, Absar Ul Haq, Manuel De La Sen. A variant of Jensen-type inequality and related results for harmonic convex functions[J]. AIMS Mathematics, 2020, 5(6): 6404-6418. doi: 10.3934/math.2020412

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Abstract

In this article, we present a variant of discrete Jensen-type inequality for harmonic convex functions and establish a Jensen-type inequality for harmonic h-convex functions. Furthermore, we found a variant of Jensen-type inequality for harmonic h-convex functions.

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