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Some Hardy-Type Inequalities For Convex Functions Via Delta Fractional Integrals

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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)

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.

Suggested Citation

  • Fuzhang Wang & Usama Hanif & Ammara Nosheen & Khuram Ali Khan & Hijaz Ahmad & Kamsing Nonlaopon, 2022. "Some Hardy-Type Inequalities For Convex Functions Via Delta Fractional Integrals," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-15, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22400047
    DOI: 10.1142/S0218348X22400047
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