Convexity with respect to strictly monotone function and Riemann-Liouville fractional Fejér-Hadamard inequalities

Shuang-Shuang Zhou; Ghulam Farid; Chahn Yong Jung; Shuang-Shuang Zhou; Ghulam Farid; Chahn Yong Jung

doi:10.3934/math.2021409

AIMS Mathematics

2021, Volume 6, Issue 7: 6975-6985. doi: 10.3934/math.2021409

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Research article

Convexity with respect to strictly monotone function and Riemann-Liouville fractional Fejér-Hadamard inequalities

1.
College of Science, Hunan City University, Yiyang 413000, China
2.
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
3.
Department of Business Administration, Gyeongsang National University, Jinju 52828, Korea

Received: 10 March 2021 Accepted: 09 April 2021 Published: 25 April 2021
MSC : 26D15, 26A33, 33E12, 26A51

In this paper we study the Fejér-Hadamard inequalities for convex function with respect to a strictly monotone function. We establish two inequalities for convex function with respect to a strictly monotone function via Riemann-Liouville fractional integrals. From inequalities found here many new results can be derived by selecting specific strictly monotone and weight functions. Also a variety of existing Fejér-Hadamard and Hadamard inequalities can be reproduced.
- Fejér-Hadamard inequality,
- convex function,
- monotone function,
- Riemann-Liouville fractional integrals
Citation: Shuang-Shuang Zhou, Ghulam Farid, Chahn Yong Jung. Convexity with respect to strictly monotone function and Riemann-Liouville fractional Fejér-Hadamard inequalities[J]. AIMS Mathematics, 2021, 6(7): 6975-6985. doi: 10.3934/math.2021409

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Abstract

In this paper we study the Fejér-Hadamard inequalities for convex function with respect to a strictly monotone function. We establish two inequalities for convex function with respect to a strictly monotone function via Riemann-Liouville fractional integrals. From inequalities found here many new results can be derived by selecting specific strictly monotone and weight functions. Also a variety of existing Fejér-Hadamard and Hadamard inequalities can be reproduced.

References

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