Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods

Abstract

<jats:p>In this current work, we introduce the finite variable additive functional equation and we derive its solution. In fact, we investigate the Hyers–Ulam stability results for the finite variable additive functional equation in fuzzy normed space by two different approaches of direct and fixed point methods.</jats:p>

Hyers–Ulam Stability of Additive Functional Equation Using Direct and Fixed-Point Methods

“…for all v ∈ Φ. Exchanging v through 2v in (13), we obtain…”

“…Czerwik [11,12] examined the stability of the quadratic functional equation involving several variables in the normed spaces. Numerous mathematicians investigated the various stability results in [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Ulam Stability and Non-Stability of Additive Functional Equation in IFN-Spaces and 2-Banach Spaces by Different Methods

“…e stability result of additive functional equations was examined by means of Najati and Moghimi [8], Shin et al [9], and Gordji [10]. Stability problems of various functional equations have been investigated by many researchers, and there are various interesting results about this problem (see [11][12][13][14]).…”

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

“…In the year 2020, Saha et al [28] applied fixed point techniques to stability problems in intuitionistic fuzzy Banach spaces. In the same year, Alanazi et al [29] proved the fuzzy stability results of a finite variable additive functional equation using direct and fixed point methods. Madadi et al [30] published ground-breaking work on the stability of unbounded differential equations in Menger k-normed spaces using a fixed point technique.…”