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

**S. Chatterjee 1, T. Bag <sup>1</sup> and Jeong-Gon Lee 2,\***


Received: 12 August 2020; Accepted: 19 September 2020; Published: 23 September 2020

**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

**MSC:** 03B52; 03E72; 46B20; 46B99; 46A19; 03E70; 15A03; 54H25
