IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i3p478-d1332241.html
   My bibliography  Save this article

A Study of Some New Hermite–Hadamard Inequalities via Specific Convex Functions with Applications

Author

Listed:
  • Moin-ud-Din Junjua

    (School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China)

  • Ather Qayyum

    (Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia)

  • Arslan Munir

    (Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Sahiwal 57000, Pakistan)

  • Hüseyin Budak

    (Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Türkiye)

  • Muhammad Mohsen Saleem

    (Department of Mathematics, Pakistan International College Jeddah, Jeddah 23342, Saudi Arabia)

  • Siti Suzlin Supadi

    (Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia)

Abstract

Convexity plays a crucial role in the development of fractional integral inequalities. Many fractional integral inequalities are derived based on convexity properties and techniques. These inequalities have several applications in different fields such as optimization, mathematical modeling and signal processing. The main goal of this article is to establish a novel and generalized identity for the Caputo–Fabrizio fractional operator. With the help of this specific developed identity, we derive new fractional integral inequalities via exponential convex functions. Furthermore, we give an application to some special means.

Suggested Citation

  • Moin-ud-Din Junjua & Ather Qayyum & Arslan Munir & Hüseyin Budak & Muhammad Mohsen Saleem & Siti Suzlin Supadi, 2024. "A Study of Some New Hermite–Hadamard Inequalities via Specific Convex Functions with Applications," Mathematics, MDPI, vol. 12(3), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:478-:d:1332241
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/3/478/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/3/478/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xiaobin Wang & Muhammad Shoaib Saleem & Kiran Naseem Aslam & Xingxing Wu & Tong Zhou & Sunil Kumar, 2020. "On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions," Journal of Mathematics, Hindawi, vol. 2020, pages 1-17, December.
    2. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-1119, July.
    Full references (including those not matched with items on IDEAS)

    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. Koessler, Frédéric & Skreta, Vasiliki, 2016. "Informed seller with taste heterogeneity," Journal of Economic Theory, Elsevier, vol. 165(C), pages 456-471.
    2. André Berger & Rudolf Müller & Seyed Hossein Naeemi, 2017. "Characterizing implementable allocation rules in multi-dimensional environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 367-383, February.
    3. Hu, Audrey & Offerman, Theo & Zou, Liang, 2011. "Premium auctions and risk preferences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2420-2439.
    4. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Mechanism design without quasilinearity," Theoretical Economics, Econometric Society, vol. 15(2), May.
    5. Peter Postl, 2013. "Efficiency versus optimality in procurement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 425-472, June.
    6. Condorelli, Daniele, 2013. "Market and non-market mechanisms for the optimal allocation of scarce resources," Games and Economic Behavior, Elsevier, vol. 82(C), pages 582-591.
    7. Manelli, Alejandro M. & Vincent, Daniel R., 2007. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly," Journal of Economic Theory, Elsevier, vol. 137(1), pages 153-185, November.
    8. Vasiliki Skreta, 2005. "Revenue Equivalence for Arbitrary Type Spaces," UCLA Economics Online Papers 347, UCLA Department of Economics.
    9. Lawrence M. Ausubel, 2006. "An Efficient Dynamic Auction for Heterogeneous Commodities," American Economic Review, American Economic Association, vol. 96(3), pages 602-629, June.
    10. X. Ruiz del Portal, 2012. "Conditions for incentive compatibility in models with multidimensional allocation functions and one-dimensional types," Review of Economic Design, Springer;Society for Economic Design, vol. 16(4), pages 311-321, December.
    11. M. Yenmez, 2015. "Incentive compatible market design with applications," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 543-569, August.
    12. Olivier Bochet, 2007. "Implementation of the Walrasian correspondence: the boundary problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 301-316, October.
    13. Alex Edmans & Xavier Gabaix, 2011. "Tractability in Incentive Contracting," The Review of Financial Studies, Society for Financial Studies, vol. 24(9), pages 2865-2894.
    14. Berger, A. & Müller, R.J. & Naeemi, S.H., 2010. "Path-monotonicity and incentive compatibility," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    15. Chatterjee, Kalyan & Vijay Krishna, R., 2011. "A nonsmooth approach to nonexpected utility theory under risk," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 166-175.
    16. Birgit Heydenreich & Rudolf Müller & Marc Uetz & Rakesh V. Vohra, 2009. "Characterization of Revenue Equivalence," Econometrica, Econometric Society, vol. 77(1), pages 307-316, January.
    17. Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2017. "Strategy-proof multi-object auction design: Ex-post revenue maximization with no wastage," ISER Discussion Paper 1001, Institute of Social and Economic Research, Osaka University.
    18. Jorge Paulo De Araújo & Marcelo De Carvalho Griebeler, 2014. "On The Integral Representation Of Thevalue Function," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 118, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    19. Levent Ülkü, 2013. "Optimal combinatorial mechanism design," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 473-498, June.
    20. Philippe Jehiel & Benny Moldovanu, 2005. "Allocative and Informational Externalities in Auctions and Related Mechanisms," Levine's Bibliography 784828000000000490, UCLA Department of Economics.

    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:12:y:2024:i:3:p:478-:d:1332241. 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.