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Some New Mathematical Integral Inequalities Pertaining to Generalized Harmonic Convexity with Applications

Author

Listed:
  • Muhammad Tariq

    (Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan
    Department of Mathematics, Baluchistan Residential College Loralai, Loralai 84800, Pakistan)

  • Soubhagya Kumar Sahoo

    (Department of Mathematics, Institute of Technical Education and Research, Siksha ‘O’ Anusandhan University, Bhubaneswar 751030, India
    Department of Mathematics, Aryan Institute of Engineering and Technology, Bhubaneswar 752050, India)

  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
    Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Omar Mutab Alsalami

    (Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Asif Ali Shaikh

    (Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan)

  • Kamsing Nonlaopon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

The subject of convex analysis and integral inequalities represents a comprehensive and absorbing field of research within the field of mathematical interpretation. In recent times, the strategies of convex theory and integral inequalities have become the subject of intensive research at historical and contemporary times because of their applications in various branches of sciences. In this work, we reveal the idea of a new version of generalized harmonic convexity i.e., an m –polynomial p –harmonic s –type convex function. We discuss this new idea by employing some examples and demonstrating some interesting algebraic properties. Furthermore, this work leads us to establish some new generalized Hermite–Hadamard- and generalized Ostrowski-type integral identities. Additionally, employing Hölder’s inequality and the power-mean inequality, we present some refinements of the H–H (Hermite–Hadamard) inequality and Ostrowski inequalities. Finally, we investigate some applications to special means involving the established results. These new results yield us some generalizations of the prior results in the literature. We believe that the methodology and concept examined in this paper will further inspire interested researchers.

Suggested Citation

  • Muhammad Tariq & Soubhagya Kumar Sahoo & Sotiris K. Ntouyas & Omar Mutab Alsalami & Asif Ali Shaikh & Kamsing Nonlaopon, 2022. "Some New Mathematical Integral Inequalities Pertaining to Generalized Harmonic Convexity with Applications," Mathematics, MDPI, vol. 10(18), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3286-:d:911610
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    References listed on IDEAS

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    1. Mihai, Marcela V. & Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some integral inequalities for harmonic h-convex functions involving hypergeometric functions," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 257-262.
    2. 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.
    3. İmdat İşcan, 2014. "Hermite-Hadamard and Simpson Type Inequalities for Differentiable P -GA-Functions," International Journal of Analysis, Hindawi, vol. 2014, pages 1-6, May.
    4. 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.
    5. İmdat İşcan, 2014. "Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions," Journal of Mathematics, Hindawi, vol. 2014, pages 1-10, June.
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