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New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators

Author

Listed:
  • Ahmet Ocak Akdemir

    (Department of Mathematics, Faculty of Science and Letters, Ağrı İbrahim Çeçen University, 04100 Ağrı, Turkey)

  • Saad Ihsan Butt

    (Lahore Campus, COMSATS University Islamabad, Islamabad 45550, Pakistan)

  • Muhammad Nadeem

    (Lahore Campus, COMSATS University Islamabad, Islamabad 45550, Pakistan)

  • Maria Alessandra Ragusa

    (Dipartimento di Matematica e Informatica, Universitá di Catania Viale Andrea Doria, 6, 95125 Catania, Italy
    RUDN University, 6 Miklukho, Maklay St., 117198 Moscow, Russia)

Abstract

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have generalized many existing results as well as iterating the Chebyshev inequality in special cases.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:122-:d:476352
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    Citations

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    Cited by:

    1. Muhammad Bilal Khan & Eze R. Nwaeze & Cheng-Chi Lee & Hatim Ghazi Zaini & Der-Chyuan Lou & Khalil Hadi Hakami, 2023. "Weighted Fractional Hermite–Hadamard Integral Inequalities for up and down Ԓ-Convex Fuzzy Mappings over Coordinates," Mathematics, MDPI, vol. 11(24), pages 1-27, December.
    2. Meshari Alesemi & Naveed Iqbal & Thongchai Botmart, 2022. "Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel," Mathematics, MDPI, vol. 10(4), pages 1-17, February.
    3. Artion Kashuri & Muhammad Samraiz & Gauhar Rahman & Zareen A. Khan, 2022. "Some New Beesack–Wirtinger-Type Inequalities Pertaining to Different Kinds of Convex Functions," Mathematics, MDPI, vol. 10(5), pages 1-20, February.
    4. Naveed Ahmed Malik & Ching-Lung Chang & Naveed Ishtiaq Chaudhary & Muhammad Asif Zahoor Raja & Khalid Mehmood Cheema & Chi-Min Shu & Sultan S. Alshamrani, 2022. "Knacks of Fractional Order Swarming Intelligence for Parameter Estimation of Harmonics in Electrical Systems," Mathematics, MDPI, vol. 10(9), pages 1-20, May.
    5. Yu, Shuhong & Zhou, Yunxiu & Du, Tingsong, 2022. "Certain midpoint-type integral inequalities involving twice differentiable generalized convex mappings and applications in fractal domain," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Saad Ihsan Butt & Josip Pečarić & Sanja Tipurić-Spužević, 2023. "Generalized Čebyšev and Grüss Type Results in Weighted Lebesgue Spaces," Mathematics, MDPI, vol. 11(7), pages 1-19, April.

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