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Some New Hermite–Hadamard Type Integral Inequalities for Twice Differentiable Generalized ((h 1, h 2); (η 1, η 2))-Convex Mappings and Their Applications

In: Frontiers in Functional Equations and Analytic Inequalities

Author

Listed:
  • Artion Kashuri

    (University Ismail Qemali of Vlora, Department of Mathematics, Faculty of Technical Science)

  • Rozana Liko

    (University Ismail Qemali of Vlora, Department of Mathematics, Faculty of Technical Science)

Abstract

In this article, we first introduced a new class of generalized ((h 1, h 2);(η 1, η 2))-convex mappings and an interesting lemma regarding Hermite–Hadamard type integral inequalities. By using the notion of generalized ((h 1, h 2);(η 1, η 2))-convexity and lemma as an auxiliary result, some new estimates difference between the left and middle part in Hermite–Hadamard type integral inequality associated with twice differentiable generalized ((h 1, h 2);(η 1, η 2))-convex mappings are established. It is pointed out that some new special cases can be deduced from main results. At the end, some applications to special means for different positive real numbers are provided.

Suggested Citation

  • Artion Kashuri & Rozana Liko, 2019. "Some New Hermite–Hadamard Type Integral Inequalities for Twice Differentiable Generalized ((h 1, h 2); (η 1, η 2))-Convex Mappings and Their Applications," Springer Books, in: George A. Anastassiou & John Michael Rassias (ed.), Frontiers in Functional Equations and Analytic Inequalities, pages 469-488, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-28950-8_24
    DOI: 10.1007/978-3-030-28950-8_24
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