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Delta Calculus on Time Scale Formulas That Are Similar to Hilbert-Type Inequalities

Author

Listed:
  • Haytham M. Rezk

    (Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt)

  • Juan E. Nápoles Valdés

    (Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Av. Libertad 5450, Corrientes 3400, Argentina)

  • Maha Ali

    (Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Sarat Ubaidah, Saudi Arabia)

  • Ahmed I. Saied

    (Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt)

  • Mohammed Zakarya

    (Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia)

Abstract

In this article, we establish some new generalized inequalities of the Hilbert-type on time scales’ delta calculus, which can be considered similar to formulas for inequalities of Hilbert type. The major innovation point is to establish some dynamic inequalities of the Hilbert-type on time scales’ delta calculus for delta differentiable functions of one variable and two variables. In this paper, we use the condition a j ( s j ) = 0 and a j ( s j , z j ) = a j ( w j , n j ) = 0 , ∀ j = 1 , 2 , … , n . These inequalities will be proved by applying Hölder’s inequality, the chain rule on time scales, and the mean inequality. As special cases of our results (when T = N and T = R ), we obtain the discrete and continuous inequalities. Also, we can obtain other inequalities in different time scales, like T = q Z − , q > 1 .

Suggested Citation

  • Haytham M. Rezk & Juan E. Nápoles Valdés & Maha Ali & Ahmed I. Saied & Mohammed Zakarya, 2023. "Delta Calculus on Time Scale Formulas That Are Similar to Hilbert-Type Inequalities," Mathematics, MDPI, vol. 12(1), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:104-:d:1308869
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    References listed on IDEAS

    as
    1. Yang, Xuehua & Wu, Lijiao & Zhang, Haixiang, 2023. "A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    2. M. Zakarya & Ahmed I.Saied & Ghada AlNemer & H. M. Rezk & Guotao Wang, 2022. "A Study on Some New Reverse Hilbert-Type Inequalities and Its Generalizations on Time Scales," Journal of Mathematics, Hindawi, vol. 2022, pages 1-18, July.
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