Some Analogies of the Banach Contraction Principle in Fuzzy Modular Spaces

Abstract

We established some theorems under the aim of deriving variants of the Banach contraction principle, using the classes of inner contractions and outer contractions, on the structure of fuzzy modular spaces.

Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

“…Shen and Chen [30] introduced the concept of fuzzy modular spaces in 2013. Further, Kumam [34,35] and Wongkum et al [36] introduced the fixed point concept in fuzzy modular spaces and obtained some properties. Wongkum and Kumam [37] investigated the Hyers-Ulam stability of sextic functional equation in fuzzy modular spaces.…”

Meir Keeler's Fixed-Point Theorem in Complex-Valued Modular Metric Space

“…Stefan Banach introduced the concept of fixed-points and subsequently established a theorem concerning the existence and uniqueness of such fixed-points within certain metric spaces. Since then, this theory has evolved by defining new types of contractions through the generalization of the mapping itself [1][2][3][4][5][6][7], as well as the generalization of the space in which this mapping is defined [8][9][10][11][12].…”

The stability of sextic functional equation in fuzzy modular spaces

“…After that, Kumam [9,10], Wongkum and et al [18] studied fixed points and some properties in modular or fuzzy modular spaces.…”

“…In this paper, we investigate the generalized Ulam-Hyers-Rassias (briefly, UHR) stability of a sextic functional equations from linear spaces into FM-spaces, by using some ideas of [2,18].…”