Fixed point technique: Hyers-Ulam stability results deriving from cubic mapping in fuzzy normed spaces
Keywords:
fuzzy normed spaces, Ulam stability, cubic mapping.Abstract
In this work, we introduce a novel finite-dimensional cubic functional equation \[ \begin{aligned} \phi\Big(\sum_{a=1}^{l}a n_{a}\Big)=\sum_{1 \leq a < b < c \leq l}\phi\Big(a n_{a}+b n_{b}+c n_{c}\Big) & +(3-l)\sum_{1 \leq a < b \leq l}\phi\Big(a n_{a}+b n_{b}\Big)\\ & +\Big(\frac{(l^{2}-5l+6)}{2}\Big)\sum_{a=0}^{l-1}(a+1)^{3}\phi(n_{a+1}) \end{aligned} \] 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.Downloads
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