AIMS Mathematics, 2020, 5(6): 6108-6123. doi: 10.3934/math.2020392.

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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

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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Keywords 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. AIMS Mathematics, 2020, 5(6): 6108-6123. doi: 10.3934/math.2020392

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