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Some New Simpson’s and Newton’s Formulas Type Inequalities for Convex Functions in Quantum Calculus

Author

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  • Pimchana Siricharuanun

    (Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand)

  • Samet Erden

    (Department of Mathematics, Faculty of Science, Bartın University, Bartın 74100, Turkey)

  • Muhammad Aamir Ali

    (Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China)

  • Hüseyin Budak

    (Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey)

  • Saowaluck Chasreechai

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Thanin Sitthiwirattham

    (Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand)

Abstract

In this paper, using the notions of q κ 2 -quantum integral and q κ 2 -quantum derivative, we present some new identities that enable us to obtain new quantum Simpson’s and quantum Newton’s type inequalities for quantum differentiable convex functions. This paper, in particular, generalizes and expands previous findings in the field of quantum and classical integral inequalities obtained by various authors.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1992-:d:618282
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Seksan Jhanthanam & Jessada Tariboon & Sotiris K. Ntouyas & Kamsing Nonlaopon, 2019. "On q -Hermite-Hadamard Inequalities for Differentiable Convex Functions," Mathematics, MDPI, vol. 7(7), pages 1-9, July.
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    Cited by:

    1. Vuk Stojiljković & Rajagopalan Ramaswamy & Ola A. Ashour Abdelnaby & Stojan Radenović, 2022. "Riemann-Liouville Fractional Inclusions for Convex Functions Using Interval Valued Setting," Mathematics, MDPI, vol. 10(19), pages 1-16, September.
    2. Fongchan Wannalookkhee & Kamsing Nonlaopon & Sotiris K. Ntouyas & Mehmet Zeki Sarikaya & Hüseyin Budak, 2022. "Some New Post-Quantum Simpson’s Type Inequalities for Coordinated Convex Functions," Mathematics, MDPI, vol. 10(6), pages 1-26, March.

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