$k$-fractional integral inequalities of Hadamard type for exponentially $(s, m)$-convex functions

Atiq Ur Rehman; Ghulam Farid; Sidra Bibi; Chahn Yong Jung; Shin Min Kang; Atiq Ur Rehman; Ghulam Farid; Sidra Bibi; Chahn Yong Jung; Shin Min Kang

doi:10.3934/math.2021052

AIMS Mathematics

2021, Volume 6, Issue 1: 882-892. doi: 10.3934/math.2021052

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Research article

$k$-fractional integral inequalities of Hadamard type for exponentially $(s, m)$-convex functions

1.
COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan
2.
Govt. Girls Primary School Kamra Khurd, Attock 43570, Pakistan
3.
Department of Business Administration, Gyeongsang National University Jinju 52828, Korea
4.
Center for General Education, China Medical University, Taichung 40402, Taiwan

Received: 29 July 2020 Accepted: 08 October 2020 Published: 03 November 2020
MSC : 26A51, 26D15, 35B05

The aim of this article is to present fractional versions of the Hadamard type inequalities for exponentially $(s, m)$-convex functions via $k$-analogue of Riemann-Liouville fractional integrals. The results provide generalizations of various known fractional integral inequalities. Some special cases are analyzed in the form of corollaries and remarks.
- convex functions,
- Hadamard inequality,
- Riemann-Liouville fractional integral operators
Citation: Atiq Ur Rehman, Ghulam Farid, Sidra Bibi, Chahn Yong Jung, Shin Min Kang. $k$-fractional integral inequalities of Hadamard type for exponentially $(s, m)$-convex functions[J]. AIMS Mathematics, 2021, 6(1): 882-892. doi: 10.3934/math.2021052

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Abstract

The aim of this article is to present fractional versions of the Hadamard type inequalities for exponentially $(s, m)$-convex functions via $k$-analogue of Riemann-Liouville fractional integrals. The results provide generalizations of various known fractional integral inequalities. Some special cases are analyzed in the form of corollaries and remarks.

References

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