Conformable integral version of Hermite-Hadamard-Fejér inequalities via <em>η</em>-convex functions

Yousaf Khurshid; Muhammad Adil Khan; Yu-Ming Chu; Yousaf Khurshid; Muhammad Adil Khan; Yu-Ming Chu

doi:10.3934/math.2020328

AIMS Mathematics

2020, Volume 5, Issue 5: 5106-5120. doi: 10.3934/math.2020328

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Research article

Conformable integral version of Hermite-Hadamard-Fejér inequalities via η-convex functions

1.
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
2.
Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
3.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China

Received: 02 May 2020 Accepted: 08 June 2020 Published: 12 June 2020
MSC : 26D15, 26A51, 26A33

The purpose of the article is to use symmetric η-convex functions to develop Hermite-Hadamard-Fejér inequality for conformable integral. We establish several conformable integral versions of Hermite-Hadamard-Fejér type inequality for the η-convex functions by use of an identity linked with Hermite-Hadamard inequality.
- η-convex function,
- Hermite-Hadamard inequality,
- Hermite-Hadamard-Fejér inequality,
- conformable derivative,
- conformable integral
Citation: Yousaf Khurshid, Muhammad Adil Khan, Yu-Ming Chu. Conformable integral version of Hermite-Hadamard-Fejér inequalities via η-convex functions[J]. AIMS Mathematics, 2020, 5(5): 5106-5120. doi: 10.3934/math.2020328

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Abstract

The purpose of the article is to use symmetric η-convex functions to develop Hermite-Hadamard-Fejér inequality for conformable integral. We establish several conformable integral versions of Hermite-Hadamard-Fejér type inequality for the η-convex functions by use of an identity linked with Hermite-Hadamard inequality.

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