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New Hermite–Hadamard and Ostrowski-Type Inequalities for Newly Introduced Co-Ordinated Convexity with Respect to a Pair of Functions

Author

Listed:
  • Muhammad Aamir Ali

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

  • Fongchan Wannalookkhee

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

  • Hüseyin Budak

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

  • Sina Etemad

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran)

  • Shahram Rezapour

    (Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
    Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Vietnam
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

Abstract

In both pure and applied mathematics, convex functions are used in many different problems. They are crucial to investigate both linear and non-linear programming issues. Since a convex function is one whose epigraph is a convex set, the theory of convex functions falls under the umbrella of convexity. However, it is a significant theory that affects practically all areas of mathematics. In this paper, we introduce the notions of g , h -convexity or convexity with respect to a pair of functions on co-ordinates and discuss its fundamental properties. Moreover, we establish some novel Hermite–Hadamard- and Ostrowski-type inequalities for newly introduced co-ordinated convexity. Additionally, it is presented that the newly introduced notion of the convexity and given inequalities are generalizations of existing studies in the literature. Lastly, we look at various mathematical examples and graphs to confirm the validity of the newly found inequalities.

Suggested Citation

  • Muhammad Aamir Ali & Fongchan Wannalookkhee & Hüseyin Budak & Sina Etemad & Shahram Rezapour, 2022. "New Hermite–Hadamard and Ostrowski-Type Inequalities for Newly Introduced Co-Ordinated Convexity with Respect to a Pair of Functions," Mathematics, MDPI, vol. 10(19), pages 1-24, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3469-:d:923057
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    References listed on IDEAS

    as
    1. İmdat İşcan, 2014. "On Some New Hermite-Hadamard Type Inequalities for s -Geometrically Convex Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-8, June.
    2. Shahram Rezapour & Sotiris K. Ntouyas & Abdelkader Amara & Sina Etemad & Jessada Tariboon, 2021. "Some Existence and Dependence Criteria of Solutions to a Fractional Integro-Differential Boundary Value Problem via the Generalized Gronwall Inequality," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    3. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Gauhar Rahman & Zafar Ullah & Aftab Khan & Erhan Set & Kottakkaran Sooppy Nisar, 2019. "Certain Chebyshev-Type Inequalities Involving Fractional Conformable Integral Operators," Mathematics, MDPI, vol. 7(4), pages 1-9, April.
    5. Feixiang Chen & Shanhe Wu, 2014. "Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, August.
    6. 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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