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

In this paper, we find the solution of the following quadratic functional equation $n{\sum }_{1\le i<j\le n}Q\left(x_i-x_j\right)={\sum }_{i=1}^{n}Q\left({\sum }_{j\ne i}{x}_j-(n-1)x_i\right)$, which is derived from the gravity of the n distinct vectors $x_1,\cdots ,x_n$ in an inner product space, and prove that the stability results of the $\mathcal{A}$-quadratic mappings in $\mu$-complete convex fuzzy modular ∗-algebras without using lower semicontinuity and $\beta$-homogeneous property. View Full-Text