IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v129y2006i2d10.1007_s10957-006-9059-y.html
   My bibliography  Save this article

On the E-Epigraph of an E-Convex Function

Author

Listed:
  • D. I. Duca

    (Babeş-Bolyai University)

  • L. Lupşa

    (Babeş-Bolyai University)

Abstract

In Ref 1, Yang shows that some of the results obtained in Ref. 2 on E-convex programming are incorrect, but does not prove that the results which make the connection between an E-convex function and its E-epigraph are incorrect. In this note, we show that the results obtained in Ref. 2 concerning the characterization of an E-convex function f in terms of its E-epigraph are incorrect. Afterward, some characterizations of E-convex functions using a different notion of epigraph are given.

Suggested Citation

  • D. I. Duca & L. Lupşa, 2006. "On the E-Epigraph of an E-Convex Function," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 341-348, May.
    • Handle: RePEc:spr:joptap:v:129:y:2006:i:2:d:10.1007_s10957-006-9059-y
    DOI: 10.1007/s10957-006-9059-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-006-9059-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-006-9059-y?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. X. M. Yang, 2001. "On E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 699-704, June.
    2. E. A. Youness, 1999. "E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 439-450, August.
    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. Babli Kumari & Anurag Jayswal, 2018. "Some properties of geodesic E-preinvex function and geodesic semi E-preinvex function on Riemannian manifolds," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 807-822, November.
    2. Akhlad Iqbal & Shahid Ali & I. Ahmad, 2012. "On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 239-251, 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. Fulga, C. & Preda, V., 2009. "Nonlinear programming with E-preinvex and local E-preinvex functions," European Journal of Operational Research, Elsevier, vol. 192(3), pages 737-743, February.
    2. Akhlad Iqbal & Shahid Ali & I. Ahmad, 2012. "On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 239-251, October.
    3. Dorel Duca & Liana Lupsa, 2012. "Saddle points for vector valued functions: existence, necessary and sufficient theorems," Journal of Global Optimization, Springer, vol. 53(3), pages 431-440, July.
    4. Babli Kumari & Anurag Jayswal, 2018. "Some properties of geodesic E-preinvex function and geodesic semi E-preinvex function on Riemannian manifolds," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 807-822, November.
    5. Tadeusz Antczak & Najeeb Abdulaleem, 2023. "On the exactness and the convergence of the $$l_{1}$$ l 1 exact penalty E-function method for E-differentiable optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1331-1359, September.
    6. Ohud Almutairi & Adem Kılıçman, 2019. "Generalized Integral Inequalities for Hermite–Hadamard-Type Inequalities via s -Convexity on Fractal Sets," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    7. Muhammad Adil Khan & Asadullah Sohail & Hidayat Ullah & Tareq Saeed, 2023. "Estimations of the Jensen Gap and Their Applications Based on 6-Convexity," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    8. Wedad Saleh & Abdelghani Lakhdari & Ohud Almutairi & Adem Kiliçman, 2023. "Some Remarks on Local Fractional Integral Inequalities Involving Mittag–Leffler Kernel Using Generalized ( E , h )-Convexity," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    9. Cristescu, Gabriela & Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2016. "Some inequalities for functions having Orlicz-convexity," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 226-236.
    10. Najeeb Abdulaleem, 2021. "Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity," SN Operations Research Forum, Springer, vol. 2(3), pages 1-18, September.

    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:spr:joptap:v:129:y:2006:i:2:d:10.1007_s10957-006-9059-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.