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Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications

Author

Listed:
  • Artion Kashuri
  • Soubhagya Kumar Sahoo
  • Bibhakar Kodamasingh
  • Muhammad Tariq
  • Ahmed A. Hamoud
  • Homan Emadifar
  • Faraidun K. Hamasalh
  • Nedal M. Mohammed
  • Masoumeh Khademi

Abstract

The main objective of this article is to introduce the notion of n–polynomial harmonically tgs–convex function and study its algebraic properties. First, we use this notion to present new variants of the Hermite–Hadamard type inequality and related integral inequalities, as well as their fractional analogues. Further, we prove two interesting integral and fractional identities for differentiable mappings, and, using them as auxiliary results, some refinements of Hermite–Hadamard type integral inequalities for both classical and fractional versions are presented. Finally, in order to show the efficiency of our results, some applications for special means and error estimations are obtained as well.

Suggested Citation

  • Artion Kashuri & Soubhagya Kumar Sahoo & Bibhakar Kodamasingh & Muhammad Tariq & Ahmed A. Hamoud & Homan Emadifar & Faraidun K. Hamasalh & Nedal M. Mohammed & Masoumeh Khademi, 2022. "Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:2493944
    DOI: 10.1155/2022/2493944
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    References listed on IDEAS

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    1. Set, Erhan & Butt, Saad Ihsan & Akdemir, Ahmet Ocak & Karaoǧlan, Ali & Abdeljawad, Thabet, 2021. "New integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. 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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