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Certain Chebyshev-Type Inequalities Involving Fractional Conformable Integral Operators

Author

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  • Gauhar Rahman

    (Department of Mathematics, Shaheed Benazir Bhutto University, Sharingal, Upper Dir, Khyber Pakhtoon Khwa 18000, Pakistan)

  • Zafar Ullah

    (Department of Mathematics, University of Education Lahore, Dera Ghazi Khan Campus 54770, Pakistan)

  • Aftab Khan

    (Department of Mathematics, Shaheed Benazir Bhutto University, Sharingal, Upper Dir, Khyber Pakhtoon Khwa 18000, Pakistan)

  • Erhan Set

    (Faculty of Science and Arts, Department of Mathematics, Ordu University, Ordu 52000, Turkey)

  • Kottakkaran Sooppy Nisar

    (Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia)

Abstract

Since an interesting functional by P.L. Chebyshev was presented in the year 1882, many results, which are called Chebyshev-type inequalities, have been established. Some of these inequalities were obtained by using fractional integral operators. Very recently, a new variant of the fractional conformable integral operator was introduced by Jarad et al. Motivated by this operator, we aim at establishing novel inequalities for a class of differentiable functions, which are associated with Chebyshev’s functional, by employing a fractional conformable integral operator. We also aim at showing important connections of the results here with those including Riemann–Liouville fractional and classical integrals.

Suggested Citation

  • Gauhar Rahman & Zafar Ullah & Aftab Khan & Erhan Set & Kottakkaran Sooppy Nisar, 2019. "Certain Chebyshev-Type Inequalities Involving Fractional Conformable Integral Operators," Mathematics, MDPI, vol. 7(4), pages 1-9, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:364-:d:224758
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    References listed on IDEAS

    as
    1. Sotiris K. Ntouyas & Sunil D. Purohit & Jessada Tariboon, 2014. "Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, May.
    2. Dumitru Baleanu & Praveen Agarwal, 2014. "Certain Inequalities Involving the Fractional -Integral Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, April.
    3. D. Baleanu & S. D. Purohit, 2014. "Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, April.
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    Cited by:

    1. Gauhar Rahman & Kottakkaran Sooppy Nisar & Thabet Abdeljawad & Samee Ullah, 2020. "Certain Fractional Proportional Integral Inequalities via Convex Functions," Mathematics, MDPI, vol. 8(2), pages 1-11, February.
    2. Gauhar Rahman & Kottakkaran Sooppy Nisar & Thabet Abdeljawad, 2020. "Tempered Fractional Integral Inequalities for Convex Functions," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    3. Gauhar Rahman & Kottakkaran Sooppy Nisar & Thabet Abdeljawad, 2020. "Certain Hadamard Proportional Fractional Integral Inequalities," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    4. Muhammad Aamir Ali & Fongchan Wannalookkhee & Hüseyin Budak & Sina Etemad & Shahram Rezapour, 2022. "New Hermite–Hadamard and Ostrowski-Type Inequalities for Newly Introduced Co-Ordinated Convexity with Respect to a Pair of Functions," Mathematics, MDPI, vol. 10(19), pages 1-24, September.

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