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Further On Opial Type Integral Inequalities For Superquadratic Functions

Author

Listed:
  • XIUJUN ZHANG

    (School of Computer Science, Chengdu University, Chengdu 610106, P. R. China)

  • GHULAM FARID

    (��Department of Mathematics, COMSATS University Islamabad, Attock 43600, Pakistan)

  • AYESHA BIBI

    (��Government Girls High School Behboodi, Hazro 43440, Pakistan)

  • KAMSING NONLAOPON

    (�Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • TAO YAN

    (School of Computer Science, Chengdu University, Chengdu 610106, P. R. China)

Abstract

The following inequality ∫0c|ψ(z)ψ′(z)|dz ≤ c 4∫0c(ψ′(z))2dz is well known in the literature as Opial’s inequality [Z. Opial, Sur une inégalité, Polon. Math. 8 (1960) 29–32], it had/has been studied extensively since its appearance. This paper investigates some of its generalizations in the prospect of generalized integral operators. From huge literature on this inequality, the results for superquadratic functions are considered and further analyzed for some integral operators. Several inequalities have been deduced for fractional integral operators by analyzing particular kernels.

Suggested Citation

  • Xiujun Zhang & Ghulam Farid & Ayesha Bibi & Kamsing Nonlaopon & Tao Yan, 2023. "Further On Opial Type Integral Inequalities For Superquadratic Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-12.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:04:n:s0218348x23400571
    DOI: 10.1142/S0218348X23400571
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