Fixed Point Technique: Hyers-Ulam Stability Results Deriving From Cubic Mapping in Fuzzy Normed Spaces - Vijaya, N.; Suganthi, P.; Bagyam, Ebenesar Anna; Balamurugan, Manivannan; Prabaharan, N.; Tamilvanan, K. (Communications in Mathematics and Applications, 2024)
In this work, we introduce a novel finite-dimensional cubic functional equation\begin{align*}\phi\Bigg(\sum\limits_{a=1}^{l}a n_{a}\Bigg)&=\sum\limits_{1 \leq a < b < c \leq l}\phi(a n_{a}+b n_{b}+c n_{c})\\&\quad +(3-l)\sum\limits_{1 \leq a < b \leq l}\phi(a n_{a}+b n_{b})\\&\quad +\Bigg(\frac{(l^{2}-5l+6)}{2}\Bigg)\sum\limits_{a=0}^{l-1}(a+1)^{3}\phi(n_{a+1}),\end{align*}where $l \geq 4$ is an integer, and derive its general solution.\ The main purpose of this work is to examine the Hyers-Ulam stability of this functional equation in fuzzy normed spaces by means of direct approach and fixed point approach.
Keywords: Fuzzy normed spaces; Ulam stability; Cubic mapping