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Bivariate Chebyshev Type Inequalities for Alpha Diamond Integrals via Time Scale Calculus

Author

Listed:
  • Khaled Aldwoah
  • Ammara Nosheen
  • Faez A. Alqarni
  • Khuram Ali Khan
  • Masud Ahmad
  • Rostin M. Mabela

Abstract

In this article, some generalizations of inequalities involving Chebyshev functional depending upon two parameters, for the class of twice differentiable functions on time scales, are studied. In order to reach the milestone, some preliminary identities are introduced involving delta and nabla integrals simultaneously. By utilizing these identities, Chebyshev type inequalities are obtained for diamond alpha integrals. Special cases are also deduced to obtain connection with existing literature.

Suggested Citation

  • Khaled Aldwoah & Ammara Nosheen & Faez A. Alqarni & Khuram Ali Khan & Masud Ahmad & Rostin M. Mabela, 2025. "Bivariate Chebyshev Type Inequalities for Alpha Diamond Integrals via Time Scale Calculus," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:7473193
    DOI: 10.1155/jom/7473193
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    References listed on IDEAS

    as
    1. Set, Erhan & Kashuri, Artion & Mumcu, İlker, 2021. "Chebyshev type inequalities by using generalized proportional Hadamard fractional integrals via Polya–Szegö inequality with applications," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Ahmet Ocak Akdemir & Saad Ihsan Butt & Muhammad Nadeem & Maria Alessandra Ragusa, 2021. "New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    3. Martin Bohner & Allan Peterson, 2001. "Dynamic Equations on Time Scales," Springer Books, Springer, number 978-1-4612-0201-1, January.
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