The stability of sextic functional equation in fuzzy modular spaces

Abstract

By using the fixed point technique, we prove the stability of sixtic functional equations. Our results are studied and proved in the framework of fuzzy modular spaces (briefly, FM-spaces). The lower semi continuous (briefly, l.s.c.) and β-homogeneous are necessary conditions for this work.

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

“…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.…”

“…for all x ∈ M, and so inequality (3.4) holds. One can easily prove the uniqueness of Q (see [37]). for all x 1 , x 2 , .…”

“…. Now, one can easily prove that {R m (f )} η-converges to A ∈ P η (see [37]). Therefore, (3.36) becomes for all x ∈ M, and hence we have…”

Ulam Type Stability of ?-Quadratic Mappings in Fuzzy Modular ∗-Algebras

“…After then, Shen and Chen [15] following the idea of probabilistic modular spaces and the definition of fuzzy metric spaces based on George and Veeramani's sense [16], applied fuzzy concept to the classical notions of modular spaces. Using Khamsi's fixed point theorem in modular spaces [17], Wongkum and Kumam [18] proved the stability of sextic functional equations in fuzzy modular spaces equipped necessarily with lower semicontinuity and β-homogeneous property.…”

Fuzzy stability of mixed type functional equations in Modular spaces

“…Kumam [11] and Wongkum et al [31] then introduced the fixed point concept in fuzzy modular spaces and obtained some of its properties. Hyers-Ulam stability of sextic functional equation in fuzzy modular spaces was scrutinized by Wongkum and Kumam [32]. Based on the notion of fuzzy modular spaces, we investigate the general solution and Hyers-Ulam stability of mixed type cubic and quartic functional equation…”