April 2023 FRACTIONAL HERMITE–HADAMARD INEQUALITY, SIMPSON’S AND OSTROWSKI’S TYPE INEQUALITIES FOR CONVEX FUNCTIONS WITH RESPECT TO A PAIR OF FUNCTIONS
Jianqiang Xie, Muhammad Aamir Ali, Hüseyin Budak, Michal Fečkan, Thanin Sitthiwirattham
Rocky Mountain J. Math. 53(2): 611-628 (April 2023). DOI: 10.1216/rmj.2023.53.611

Abstract

We consider the convexity with respect to a pair of functions and establish a Hermite–Hadamard type inequality for Riemann–Liouville fractional integrals. Moreover, we derive some new Simpson’s and Ostrowski’s type inequalities for differentiable convex mapping with respect to a pair of functions. We also show that the newly established inequalities are the extension of some existing inequalities. Finally, we consider some mathematical examples and graphs to show the validity of the newly established inequalities.

Citation

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Jianqiang Xie. Muhammad Aamir Ali. Hüseyin Budak. Michal Fečkan. Thanin Sitthiwirattham. "FRACTIONAL HERMITE–HADAMARD INEQUALITY, SIMPSON’S AND OSTROWSKI’S TYPE INEQUALITIES FOR CONVEX FUNCTIONS WITH RESPECT TO A PAIR OF FUNCTIONS." Rocky Mountain J. Math. 53 (2) 611 - 628, April 2023. https://doi.org/10.1216/rmj.2023.53.611

Information

Received: 26 April 2022; Revised: 9 May 2022; Accepted: 11 May 2022; Published: April 2023
First available in Project Euclid: 20 June 2023

MathSciNet: MR4604777
Digital Object Identifier: 10.1216/rmj.2023.53.611

Subjects:
Primary: 26A51‎ , 26D10 , 26D15

Keywords: (g,h)-convex functions , Fractional calculus , Hermite–Hadamard inequality , Ostrowski’s inequality , Simpson’s inequality

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 2 • April 2023
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