AIMS Mathematics, 2020, 5(5): 4781-4792. doi: 10.3934/math.2020306.

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Derivation of bounds of integral operators via convex functions

1 Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing, Jiangsu, China
2 Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
3 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India
4 Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
5 Department of Mathematics, Air Univeristy, Islamabad, Pakistan

Convex functions play a vital role in the derivation of inequalities. In this paper these functions are used to obtain certain bounds of a unified integral operator. A Hadamard inequality for these operators is established. Further bounds of several kinds of fractional and conformable integral operators are deduced in particular.
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Keywords integral operators; fractional integrals; convex functions; bounds

Citation: Xinghua You, Ghulam Farid, Lakshmi Narayan Mishra, Kahkashan Mahreen, Saleem Ullah. Derivation of bounds of integral operators via convex functions. AIMS Mathematics, 2020, 5(5): 4781-4792. doi: 10.3934/math.2020306


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