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

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
• <i>t</i>-norm
• measure of non-compactness