IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i10p1643-d417994.html
   My bibliography  Save this article

Schauder-Type Fixed Point Theorem in Generalized Fuzzy Normed Linear Spaces

Author

Listed:
  • S. Chatterjee

    (Department of Mathematics, Siksha-Bhavana, Visva-Bharati, Santiniketan, Birbhum, West-Bengal 731235, India)

  • T. Bag

    (Department of Mathematics, Siksha-Bhavana, Visva-Bharati, Santiniketan, Birbhum, West-Bengal 731235, India)

  • Jeong-Gon Lee

    (Division of Applied Mathematics, Wonkwang University, 460, Iksan-daero, Iksan-Si, Jeonbuk 54538, Korea)

Abstract

In the present article, the Schauder-type fixed point theorem for the class of fuzzy continuous, as well as fuzzy compact operators is established in a fuzzy normed linear space (fnls) whose underlying t -norm is left-continuous at ( 1 , 1 ) . In the fuzzy setting, the concept of the measure of non-compactness is introduced, and some basic properties of the measure of non-compactness are investigated. Darbo’s generalization of the Schauder-type fixed point theorem is developed for the class of ψ -set contractions. This theorem is proven by using the idea of the measure of non-compactness.

Suggested Citation

  • S. Chatterjee & T. Bag & Jeong-Gon Lee, 2020. "Schauder-Type Fixed Point Theorem in Generalized Fuzzy Normed Linear Spaces," Mathematics, MDPI, vol. 8(10), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1643-:d:417994
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/10/1643/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/10/1643/
    Download Restriction: no
    ---><---

    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:8:y:2020:i:10:p:1643-:d:417994. 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: 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.