AIMS Mathematics, 2020, 5(6): 5510-5520. doi: 10.3934/math.2020353.

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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

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.
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Keywords 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. AIMS Mathematics, 2020, 5(6): 5510-5520. doi: 10.3934/math.2020353

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