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Certain Results Comprising the Weighted Chebyshev Function Using Pathway Fractional Integrals

Author

Listed:
  • Aditya Mani Mishra

    (Department of HEAS (Mathematics), Rajasthan Technical University, Kota 324010, India)

  • Dumitru Baleanu

    (Department of Mathematics, Cankaya University, Cankaya, Ankara 06430, Turkey
    Institute of Space Sciences, Magurele-Bucharest R7690, Romania)

  • Fairouz Tchier

    (Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia)

  • Sunil Dutt Purohit

    (Department of HEAS (Mathematics), Rajasthan Technical University, Kota 324010, India)

Abstract

An analogous version of Chebyshev inequality, associated with the weighted function, has been established using the pathway fractional integral operators. The result is a generalization of the Chebyshev inequality in fractional integral operators. We deduce the left sided Riemann Liouville version and the Laplace version of the same identity. Our main deduction will provide noted results for an appropriate change to the Pathway fractional integral parameter and the degree of the fractional operator.

Suggested Citation

  • Aditya Mani Mishra & Dumitru Baleanu & Fairouz Tchier & Sunil Dutt Purohit, 2019. "Certain Results Comprising the Weighted Chebyshev Function Using Pathway Fractional Integrals," Mathematics, MDPI, vol. 7(10), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:896-:d:270559
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    References listed on IDEAS

    as
    1. Mathai, A.M. & Haubold, H.J., 2007. "Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 110-122.
    2. 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.
    3. Dumitru Baleanu & Praveen Agarwal, 2014. "Certain Inequalities Involving the Fractional -Integral Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, April.
    4. 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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