IDEAS home Printed from https://ideas.repec.org/h/spr/spochp/978-3-030-84122-5_35.html
   My bibliography  Save this book chapter

General Preinvex Functions and Variational-Like Inequalities

In: Approximation and Computation in Science and Engineering

Author

Listed:
  • Muhammad Aslam Noor

    (COMSATS University Islamabad)

  • Khalida Inayat Noor

    (COMSATS University Islamabad)

  • Bandar Mohsen

    (King Saud University)

  • Michael Th. Rassias

    (University of Zurich)

  • Andrei Raigorodskii

    (Moscow Institute of Physics and Technology
    Moscow State University
    Buryat State University
    Adyghe State University)

Abstract

In this paper, we define and introduce some new concepts of the higher order strongly general preinvex functions and higher order strongly monotone operators involving the arbitrary bifunction. Some new relationships among various concepts of higher order strongly general preinvex functions have been established. It is shown that the new parallelogram laws for Banach spaces can be obtained as applications of higher order strongly affine general preinvex functions, which is itself a novel application. It is proved that the optimality conditions of the higher order strongly general preinvex functions are characterized by a class of variational inequalities, which are called the higher order strongly general variational-like inequalities. An auxiliary principle technique is used to suggest an implicit method for solving strongly general variational-like inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. Some special cases are also discussed. Results obtained in this paper can be viewed as a refinement and improvement of previously known results.

Suggested Citation

  • Muhammad Aslam Noor & Khalida Inayat Noor & Bandar Mohsen & Michael Th. Rassias & Andrei Raigorodskii, 2022. "General Preinvex Functions and Variational-Like Inequalities," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Approximation and Computation in Science and Engineering, pages 643-666, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-84122-5_35
    DOI: 10.1007/978-3-030-84122-5_35
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

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


    Cited by:

    1. Peter Hubert Mathieu Mouche & Ferenc Szidarovszky, 2023. "Aggregative Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1056-1092, March.
    2. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Class of Preinvex Fuzzy Mappings and Related Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-20, October.

    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:spr:spochp:978-3-030-84122-5_35. 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: 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.