Some unified bounds for exponentially $tgs$-convex functions governed by conformable fractional operators

Hu Ge-JiLe; Saima Rashid; Muhammad Aslam Noor; Arshiya Suhail; Yu-Ming Chu; Hu Ge-JiLe; Saima Rashid; Muhammad Aslam Noor; Arshiya Suhail; Yu-Ming Chu

doi:10.3934/math.2020392

AIMS Mathematics

2020, Volume 5, Issue 6: 6108-6123. doi: 10.3934/math.2020392

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Research article

Some unified bounds for exponentially $tgs$-convex functions governed by conformable fractional operators

1.
School of Science, Huzhou University, Huzhou 313000, P. R. China
2.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
3.
Department of Mathematics, COMSATS University, Islamabad 44000, 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

Received: 15 March 2020 Accepted: 15 July 2020 Published: 28 July 2020
MSC : 26D15, 26D10, 90C23

In the article, we introduce the concept of the exponentially $tgs$-convex function and discover two new conformable fractional integral identities concerning the first-order differentiable convex mappings. By using these identities, we establish several new right-sided Hermite-Hadamard type inequalities for the exponentially $tgs$-convex functions via conformable fractional integrals. Our outcomes for conformable fractional integral operators are also applied to some special means.
- integral inequality,
- exponentially $tgs$-convex function,
- conformable fractional integral operator,
- Hermite-Hadamard inequality
Citation: Hu Ge-JiLe, Saima Rashid, Muhammad Aslam Noor, Arshiya Suhail, Yu-Ming Chu. Some unified bounds for exponentially $tgs$-convex functions governed by conformable fractional operators[J]. AIMS Mathematics, 2020, 5(6): 6108-6123. doi: 10.3934/math.2020392

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Abstract

In the article, we introduce the concept of the exponentially $tgs$-convex function and discover two new conformable fractional integral identities concerning the first-order differentiable convex mappings. By using these identities, we establish several new right-sided Hermite-Hadamard type inequalities for the exponentially $tgs$-convex functions via conformable fractional integrals. Our outcomes for conformable fractional integral operators are also applied to some special means.

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