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

S. Chatterjee, T. Bag and Jeong-Gon Lee
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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

Mathematics, 2020, vol. 8, issue 10, 1-18

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.

Keywords: Schauder fixed point theorem; fuzzy normed linear space; t -norm; measure of non-compactness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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