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Some quantum integral inequalities via preinvex functions

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  • Noor, Muhammad Aslam
  • Noor, Khalida Inayat
  • Awan, Muhammad Uzair

Abstract

In this paper, we obtain some new quantum analogues of Hermite–Hadamard and Iyengar type inequalities for some classes of preinvex functions. Some special cases are also discussed.

Suggested Citation

  • Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some quantum integral inequalities via preinvex functions," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 242-251.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:242-251
    DOI: 10.1016/j.amc.2015.07.078
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    References listed on IDEAS

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    1. Tadeusz Antczak, 2014. "On efficiency and mixed duality for a new class of nonconvex multiobjective variational control problems," Journal of Global Optimization, Springer, vol. 59(4), pages 757-785, August.
    2. Ariana Pitea & Mihai Postolache, 2012. "Duality theorems for a new class of multitime multiobjective variational problems," Journal of Global Optimization, Springer, vol. 54(1), pages 47-58, September.
    3. Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some quantum estimates for Hermite–Hadamard inequalities," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 675-679.
    4. X.M. Yang & X.Q. Yang & K.L. Teo, 2003. "Generalized Invexity and Generalized Invariant Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 607-625, June.
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    Cited by:

    1. Aglić Aljinović, Andrea & Kovačević, Domagoj & Puljiz, Mate & Žgaljić Keko, Ana, 2021. "On Ostrowski inequality for quantum calculus," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Muhammad Aamir Ali & Sotiris K. Ntouyas & Jessada Tariboon, 2021. "Generalization of Quantum Ostrowski-Type Integral Inequalities," Mathematics, MDPI, vol. 9(10), pages 1-8, May.
    3. Surang Sitho & Muhammad Aamir Ali & Hüseyin Budak & Sotiris K. Ntouyas & Jessada Tariboon, 2021. "Trapezoid and Midpoint Type Inequalities for Preinvex Functions via Quantum Calculus," Mathematics, MDPI, vol. 9(14), pages 1-21, July.
    4. Yongping Deng & Muhammad Uzair Awan & Shanhe Wu, 2019. "Quantum Integral Inequalities of Simpson-Type for Strongly Preinvex Functions," Mathematics, MDPI, vol. 7(8), pages 1-14, August.
    5. Hefeng Zhuang & Wenjun Liu & Jaekeun Park, 2019. "Some Quantum Estimates of Hermite-Hadamard Inequalities for Quasi-Convex Functions," Mathematics, MDPI, vol. 7(2), pages 1-18, February.
    6. Humaira Kalsoom & Muhammad Amer & Moin-ud-Din Junjua & Sabir Hussain & Gullnaz Shahzadi, 2019. "Some ( p , q )-Estimates of Hermite-Hadamard-Type Inequalities for Coordinated Convex and Quasi- Convex Functions," Mathematics, MDPI, vol. 7(8), pages 1-22, July.
    7. Pimchana Siricharuanun & Samet Erden & Muhammad Aamir Ali & Hüseyin Budak & Saowaluck Chasreechai & Thanin Sitthiwirattham, 2021. "Some New Simpson’s and Newton’s Formulas Type Inequalities for Convex Functions in Quantum Calculus," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    8. Cristescu, Gabriela & Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2016. "Some inequalities for functions having Orlicz-convexity," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 226-236.
    9. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Class of Preinvex Fuzzy Mappings and Related Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-20, October.

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