On new generalized quantum integrals and related Hermite–Hadamard inequalities View Full Text


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Article Info

DATE

2021-10-30

AUTHORS

Hasan Kara, Hüseyin Budak, Necmettin Alp, Humaira Kalsoom, Mehmet Zeki Sarikaya

ABSTRACT

In this article, we introduce a new concept of quantum integrals which is called Tqκ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${}^{\kappa _{2}}T_{q}$\end{document}-integral. Then we prove several properties of this concept of quantum integrals. Moreover, we present several Hermite–Hadamard type inequalities for Tqκ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${}^{\kappa _{2}}T_{q}$\end{document}-integral by utilizing differentiable convex functions. The results presented in this article are unification and generalization of the comparable results in the literature. More... »

PAGES

180

References to SciGraph publications

  • 2002. Quantum Calculus in NONE
  • 2020-02-14. On q-Hermite–Hadamard inequalities for general convex functions in ACTA MATHEMATICA HUNGARICA
  • 2012. A Comprehensive Treatment of q-Calculus in NONE
  • 2003. A Method for q-Calculus in JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
  • 2013-11-07. Quantum calculus on finite intervals and applications to impulsive difference equations in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2014-03-26. Quantum integral inequalities on finite intervals in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2011-03-10. Fractional Quantum Integral Inequalities in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1186/s13660-021-02715-7

    DOI

    http://dx.doi.org/10.1186/s13660-021-02715-7

    DIMENSIONS

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