Fuzzy Stability of a Generalized 4-Dimensional AQCQ Functional Equation

Abstract

Functional equations are widely used in various fields for solving practical examples, exploring theoretical ideas, and modeling complex relationships and the study of their stability is essential for understanding how small changes in the inputs or functional form affect the solutions. This has both theoretical significances and practical applications across mathematics, science, and engineering. For this purpose,
in this paper, we explore the Ulam-Hyers stability of
\begin{align*}
&\Lambda\left( z_1 + z_2+ \lambda\left( z_3+ z_4\right)\right)
+ \Lambda\left( z_1 + z_2 - \lambda\left( z_3+ z_4\right)\right)\notag\\
& ~~~= \lambda^{2} \Big\{\Lambda\left( z_1 + z_2 + z_3+ z_4\right) + \Lambda\left( z_1 + z_2 - z_3 - z_4\right)\Big\}
+2\left(1 - \lambda^{2}\right) \Lambda\left( z_1 +z_2\right) \notag\\
&\qquad + \frac{\left(\lambda^{4} -\lambda^{2} \right)}{12} \Big\{
\Lambda\left( 2\left( z_3+ z_4\right)\right) +\Lambda\left( - 2 \left( z_3+ z_4\right)\right)
- 4 \left(
\Lambda\left( z_3+ z_4\right) +\Lambda\left( - z_3 - z_4\right)\right)\Big\},
\end{align*}
a generalized 4-dimensional AQCQ functional equation in fuzzy normed spaces using two different methods.