Derivation of bounds of integral operators via convex functions

Xinghua You; Ghulam Farid; Lakshmi Narayan Mishra; Kahkashan Mahreen; Saleem Ullah; Xinghua You; Ghulam Farid; Lakshmi Narayan Mishra; Kahkashan Mahreen; Saleem Ullah

doi:10.3934/math.2020306

AIMS Mathematics

2020, Volume 5, Issue 5: 4781-4792. doi: 10.3934/math.2020306

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Research article

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

Received: 01 December 2019 Accepted: 25 May 2020 Published: 02 June 2020
MSC : 26A33, 26D10, 31A10

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

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Abstract

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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