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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

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Frontiers in Functional Equations and Analytic Inequalities

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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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Technical Science, University Ismail Qemali of Vlora, Vlora, Albania

    Artion Kashuri & Rozana Liko

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  1. Artion Kashuri
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  2. Rozana Liko
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Editors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA

    George A. Anastassiou

  2. Pedagogical Department E. E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens, Athens, Greece

    John Michael Rassias

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Kashuri, A., Liko, R. (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. In: Anastassiou, G., Rassias, J. (eds) Frontiers in Functional Equations and Analytic Inequalities. Springer, Cham. https://doi.org/10.1007/978-3-030-28950-8_24

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