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Hermite-Hadamard Type Inequalities for Interval ( h 1 , h 2 )-Convex Functions

Author

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  • Yanrong An

    (School of Business, Nanjing University, Nanjing 210098, China)

  • Guoju Ye

    (College of Science, Hohai University, Nanjing 210098, China)

  • Dafang Zhao

    (School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China)

  • Wei Liu

    (College of Science, Hohai University, Nanjing 210098, China)

Abstract

We introduce the concept of interval ( h 1 , h 2 ) -convex functions. Under the new concept, we establish some new interval Hermite-Hadamard type inequalities, which generalize those in the literature. Also, we give some interesting examples.

Suggested Citation

  • Yanrong An & Guoju Ye & Dafang Zhao & Wei Liu, 2019. "Hermite-Hadamard Type Inequalities for Interval ( h 1 , h 2 )-Convex Functions," Mathematics, MDPI, vol. 7(5), pages 1-9, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:436-:d:232061
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    References listed on IDEAS

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    1. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    2. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    3. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    4. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 1.
    5. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    6. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    7. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
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    Citations

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    Cited by:

    1. Tareq Saeed & Muhammad Bilal Khan & Savin Treanță & Hamed H. Alsulami & Mohammed Sh. Alhodaly, 2023. "Study of Log Convex Mappings in Fuzzy Aunnam Calculus via Fuzzy Inclusion Relation over Fuzzy-Number Space," Mathematics, MDPI, vol. 11(9), pages 1-16, April.
    2. Muhammad Bilal Khan & Savin Treanțǎ & Mohamed S. Soliman & Kamsing Nonlaopon & Hatim Ghazi Zaini, 2022. "Some New Versions of Integral Inequalities for Left and Right Preinvex Functions in the Interval-Valued Settings," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    3. Tareq Saeed & Waqar Afzal & Mujahid Abbas & Savin Treanţă & Manuel De la Sen, 2022. "Some New Generalizations of Integral Inequalities for Harmonical cr -( h 1 , h 2 )-Godunova–Levin Functions and Applications," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    4. Muhammad Bilal Khan & Gustavo Santos-García & Hatim Ghazi Zaini & Savin Treanță & Mohamed S. Soliman, 2022. "Some New Concepts Related to Integral Operators and Inequalities on Coordinates in Fuzzy Fractional Calculus," Mathematics, MDPI, vol. 10(4), pages 1-26, February.
    5. Tareq Saeed & Waqar Afzal & Khurram Shabbir & Savin Treanţă & Manuel De la Sen, 2022. "Some Novel Estimates of Hermite–Hadamard and Jensen Type Inequalities for ( h 1 , h 2 )-Convex Functions Pertaining to Total Order Relation," Mathematics, MDPI, vol. 10(24), pages 1-17, December.
    6. Muhammad Bilal Khan & Hakeem A. Othman & Aleksandr Rakhmangulov & Mohamed S. Soliman & Alia M. Alzubaidi, 2023. "Discussion on Fuzzy Integral Inequalities via Aumann Integrable Convex Fuzzy-Number Valued Mappings over Fuzzy Inclusion Relation," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    7. Waqar Afzal & Alina Alb Lupaş & Khurram Shabbir, 2022. "Hermite–Hadamard and Jensen-Type Inequalities for Harmonical ( h 1 , h 2 )-Godunova–Levin Interval-Valued Functions," Mathematics, MDPI, vol. 10(16), pages 1-16, August.

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