SOME HARDY-TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA DELTA FRACTIONAL INTEGRALS

Fuzhang Wang, Usama Hanif (), Ammara Nosheen (), Khuram Ali Khan (), Hijaz Ahmad and Kamsing Nonlaopon
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Fuzhang Wang: School of Mathematical and Statistics, Xuzhou University of Technology, Xuzhou 2221018, Jiangsu, China†Nanchang Institute of Technology, Nanchang 330044, China‡College of Mathematics, Huaibei Normal University, Huaibei 235000, China
Usama Hanif: �Department of Mathematics & Statistics, The University of Lahore, Sargodha, Campus, Sargodha, Pakistan
Ammara Nosheen: �Department of Mathematics & Statistics, The University of Lahore, Sargodha, Campus, Sargodha, Pakistan
Khuram Ali Khan: �Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan
Hijaz Ahmad: ��Department of Basic Sciences, University of Engineering and Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan**Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio, Emanuele II, 39, 00186 Roma, Italy
Kamsing Nonlaopon: ��†Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-15

Abstract: In this paper, some Jensen- and Hardy-type inequalities for convex functions are extended by using Riemann–Liouville delta fractional integrals. Further, some Pólya–Knopp-type inequalities and Hardy–Hilbert-type inequality for convex functions are also proved. Moreover, some related inequalities are proved by using special kernels. Particular cases of resulting inequalities provide the results on fractional calculus, time scales calculus, quantum fractional calculus and discrete fractional calculus.

Keywords: Time Scales Calculus; Fractional Calculus; Hardy-Type Inequalities; Jensen’s Inequality (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400047

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