IDEAS home Printed from https://ideas.repec.org/a/hin/jjmath/346305.html

Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions

Author

Listed:
  • İmdat İşcan

Abstract

A new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite-Hadamard and Simpson-like types for functions whose derivatives in absolute value at certain power are harmonically convex. Some applications to special means of real numbers are also given.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jjmath:346305
    DOI: 10.1155/2014/346305
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JMATH/2014/346305.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JMATH/2014/346305.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/346305?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Feixiang Chen & Shanhe Wu, 2014. "Fejér and Hermite‐Hadamard Type Inequalities for Harmonically Convex Functions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Praveen Agarwal & Mahir Kadakal & İmdat İşcan & Yu-Ming Chu, 2020. "Better Approaches for n -Times Differentiable Convex Functions," Mathematics, MDPI, vol. 8(6), pages 1-11, June.
    3. Sabila Ali & Muhammad Samraiz & Saima Naheed & Miguel Vivas-Cortez, 2025. "Advancements in Harmonic Convexity and Its Role in Modern Mathematical Analysis," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    4. Saima Rashid & Aasma Khalid & Omar Bazighifan & Georgia Irina Oros, 2021. "New Modifications of Integral Inequalities via ℘ -Convexity Pertaining to Fractional Calculus and Their Applications," Mathematics, MDPI, vol. 9(15), pages 1-23, July.
    5. Asfand Fahad & Shigeru Furuichi & Zammad Ali & Yuanheng Wang, 2025. "Novel extensions of k-harmonically convex functions and their applications in information science," PLOS ONE, Public Library of Science, vol. 20(7), pages 1-18, July.
    6. Imran Abbas Baloch & İmdat İşcan, 2015. "Some Ostrowski Type Inequalities for Harmonically -Convex Functions in Second Sense," International Journal of Analysis, Hindawi, vol. 2015, pages 1-9, October.
    7. Yeliang Xiao & Muhammad Shoaib Saleem & Faiza Batool, 2022. "Some Fractional Integral Inequalities for a Generalized Class of Nonconvex Functions," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    8. Kamsing Nonlaopon & Ghulam Farid & Ammara Nosheen & Muhammad Yussouf & Ebenezer Bonyah, 2022. "New Generalized Riemann–Liouville Fractional Integral Versions of Hadamard and Fejér–Hadamard Inequalities," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    9. Shin Min Kang & Ghulam Abbas & Ghulam Farid & Waqas Nazeer, 2018. "A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results," Mathematics, MDPI, vol. 6(7), pages 1-16, July.
    10. Hüseyin Budak & Fatih Hezenci & Hasan Kara & Mehmet Zeki Sarikaya, 2023. "Bounds for the Error in Approximating a Fractional Integral by Simpson’s Rule," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    11. Xia Wu & JinRong Wang & Jialu Zhang, 2019. "Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel," Mathematics, MDPI, vol. 7(9), pages 1-12, September.
    12. Muhammad Tariq & Soubhagya Kumar Sahoo & Sotiris K. Ntouyas & Omar Mutab Alsalami & Asif Ali Shaikh & Kamsing Nonlaopon, 2022. "Some New Mathematical Integral Inequalities Pertaining to Generalized Harmonic Convexity with Applications," Mathematics, MDPI, vol. 10(18), pages 1-21, September.
    13. Artion Kashuri & Soubhagya Kumar Sahoo & Bibhakar Kodamasingh & Muhammad Tariq & Ahmed A. Hamoud & Homan Emadifar & Faraidun K. Hamasalh & Nedal M. Mohammed & Masoumeh Khademi, 2022. "Integral Inequalities of Integer and Fractional Orders for n–Polynomial Harmonically tgs–Convex Functions and Their Applications," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    14. Abdul Mateen & Bandar Bin-Mohsin & Ghulam Hussain Tipu & Asia Shehzadi, 2025. "Error Estimation of Weddle’s Rule for Generalized Convex Functions with Applications to Numerical Integration and Computational Analysis," Mathematics, MDPI, vol. 13(17), pages 1-18, September.
    15. Yahya Almalki & Waqar Afzal, 2023. "Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr - h -Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    16. 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.
    17. Dafang Zhao & Ghazala Gulshan & Muhammad Aamir Ali & Kamsing Nonlaopon, 2022. "Some New Midpoint and Trapezoidal-Type Inequalities for General Convex Functions in q -Calculus," Mathematics, MDPI, vol. 10(3), pages 1-14, January.
    18. Fangfang Shi & Guoju Ye & Dafang Zhao & Wei Liu, 2020. "Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    19. 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.
    20. 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.
    21. 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.
    22. Muhammad Bilal Khan & Aleksandr Rakhmangulov & Najla Aloraini & Muhammad Aslam Noor & Mohamed S. Soliman, 2023. "Generalized Harmonically Convex Fuzzy-Number-Valued Mappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    23. Bandar Bin Mohsin & Muhammad Uzair Awan & Muhammad Zakria Javed & Hüseyin Budak & Awais Gul Khan & Muhammad Aslam Noor, 2022. "Inclusions Involving Interval‐Valued Harmonically Co‐Ordinated Convex Functions and Raina’s Fractional Double Integrals," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jjmath:346305. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.