Fractional version of the Jensen-Mercer and Hermite-Jensen-Mercer type inequalities for strongly h-convex function

Fangfang Ma; Fangfang Ma

doi:10.3934/math.2022047

AIMS Mathematics

2022, Volume 7, Issue 1: 784-803. doi: 10.3934/math.2022047

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Research article

Fractional version of the Jensen-Mercer and Hermite-Jensen-Mercer type inequalities for strongly h-convex function

Fangfang Ma ^,

Department of Foundational Course, Shandong University of Science and Technology, Taian 271019 China

Received: 13 July 2021 Accepted: 27 September 2021 Published: 18 October 2021
MSC : 35A23, 26E70, 34N05

In this paper we find further versions of generalized Hadamard type fractional integral inequality for $ k $-fractional integrals. For this purpose we utilize the definition of $ h $-convex function. The presented results hold simultaneously for variant types of convexities and fractional integrals.
- convex function,
- Hermite-Hadamard inequality,
- Jensen-Mercer inequality,
- fractional integrals
Citation: Fangfang Ma. Fractional version of the Jensen-Mercer and Hermite-Jensen-Mercer type inequalities for strongly h-convex function[J]. AIMS Mathematics, 2022, 7(1): 784-803. doi: 10.3934/math.2022047

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Abstract

In this paper we find further versions of generalized Hadamard type fractional integral inequality for $ k $-fractional integrals. For this purpose we utilize the definition of $ h $-convex function. The presented results hold simultaneously for variant types of convexities and fractional integrals.

References

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