Certain exponential type $ m $-convexity inequalities for fractional integrals with exponential kernels

Hao Wang; Zhijuan Wu; Xiaohong Zhang; Shubo Chen; Hao Wang; Zhijuan Wu; Xiaohong Zhang; Shubo Chen

doi:10.3934/math.2022351

AIMS Mathematics

2022, Volume 7, Issue 4: 6311-6330. doi: 10.3934/math.2022351

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Research article

Certain exponential type $ m $-convexity inequalities for fractional integrals with exponential kernels

Department of Mathematics, College of Science, Hunan City University, Yiyang 413000, China

Received: 09 November 2021 Revised: 29 December 2021 Accepted: 11 January 2022 Published: 19 January 2022
MSC : 26D15, 26A51, 26E60, 60E15

By applying exponential type $ m $-convexity, the Hölder inequality and the power mean inequality, this paper is devoted to conclude explicit bounds for the fractional integrals with exponential kernels inequalities, such as right-side Hadamard type, midpoint type, trapezoid type and Dragomir-Agarwal type inequalities. The results of this study are obtained for mappings $ \omega $ where $ \omega $ and $ |\omega'| $ (or $ |\omega'|^q $with $ q\geq 1 $) are exponential type $ m $-convex. Also, the results presented in this article provide generalizations of those given in earlier works.
- Hermite-Hadamard type inequality,
- fractional integrals,
- exponential type $ m $-convex mappings
Citation: Hao Wang, Zhijuan Wu, Xiaohong Zhang, Shubo Chen. Certain exponential type $ m $-convexity inequalities for fractional integrals with exponential kernels[J]. AIMS Mathematics, 2022, 7(4): 6311-6330. doi: 10.3934/math.2022351

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Abstract

By applying exponential type $ m $-convexity, the Hölder inequality and the power mean inequality, this paper is devoted to conclude explicit bounds for the fractional integrals with exponential kernels inequalities, such as right-side Hadamard type, midpoint type, trapezoid type and Dragomir-Agarwal type inequalities. The results of this study are obtained for mappings $ \omega $ where $ \omega $ and $ |\omega'| $ (or $ |\omega'|^q $with $ q\geq 1 $) are exponential type $ m $-convex. Also, the results presented in this article provide generalizations of those given in earlier works.

References

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