IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i9p845-d266802.html
   My bibliography  Save this article

Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel

Author

Listed:
  • Xia Wu

    (School of Mathematics and Finance, Xiangnan University, Chenzhou 411105, China)

  • JinRong Wang

    (Department of Mathematics, Guizhou University, Guiyang 550025, China
    School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

  • Jialu Zhang

    (School of Mathematics and Finance, Xiangnan University, Chenzhou 411105, China)

Abstract

In this paper, we establish three fundamental integral identities by the first- and second-order derivatives for a given function via the fractional integrals with exponential kernel. With the help of these new fractional integral identities, we introduce a few interesting Hermite–Hadamard-type inequalities involving left-sided and right-sided fractional integrals with exponential kernels for convex functions. Finally, some applications to special means of real number are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:845-:d:266802
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/9/845/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/9/845/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Muhammad Bilal Khan & Jorge E. Macías-Díaz & Savin Treanțǎ & Mohamed S. Soliman, 2022. "Some Fejér-Type Inequalities for Generalized Interval-Valued Convex Functions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    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. 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.
    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. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.

    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:gam:jmathe:v:7:y:2019:i:9:p:845-:d:266802. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.