Bounds of a unified integral operator for (<em>s</em>,<em>m</em>)-convex functions and their consequences

Zitong He; Xiaolin Ma; Ghulam Farid; Absar Ul Haq; Kahkashan Mahreen; Zitong He; Xiaolin Ma; Ghulam Farid; Absar Ul Haq; Kahkashan Mahreen

doi:10.3934/math.2020353

AIMS Mathematics

2020, Volume 5, Issue 6: 5510-5520. doi: 10.3934/math.2020353

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Research article

Bounds of a unified integral operator for (s,m)-convex functions and their consequences

1.
School of business administration, University of science and technology Liaoning, Anshan 114051, China
2.
Department of mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
3.
Department of Basic Science and Humanities, University of Engineering and Technology, Lahore (Narowal Campus), Pakistan

Received: 25 January 2020 Accepted: 18 June 2020 Published: 28 June 2020
MSC : 26D10, 31A10, 26A33

The unified integral operator presented in Definition 4 produces several kinds of known fractional and conformable integral operators. The goal of this paper is to obtain bounds of this unified integral operator by using the definition of (s, m)-convexity. The resulting inequalities in specific cases represent the bounds of many known fractional and conformable fractional integral operators in a compact form.
- integral operators,
- fractional integral operators,
- conformable integral operators,
- convex functions,
- bounds
Citation: Zitong He, Xiaolin Ma, Ghulam Farid, Absar Ul Haq, Kahkashan Mahreen. Bounds of a unified integral operator for (s,m)-convex functions and their consequences[J]. AIMS Mathematics, 2020, 5(6): 5510-5520. doi: 10.3934/math.2020353

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Abstract

The unified integral operator presented in Definition 4 produces several kinds of known fractional and conformable integral operators. The goal of this paper is to obtain bounds of this unified integral operator by using the definition of (s, m)-convexity. The resulting inequalities in specific cases represent the bounds of many known fractional and conformable fractional integral operators in a compact form.

References

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