On the generalized A-quadratic mappings associated with the variance of a discrete-type distribution

In this paper, we prove the Hyers-Ulam-Rassias stability of the following generalized quadratic functional equation of Euler-Lagrange type ∑i=1nriQ∑j=1nrj(xi-xj)+∑i=1nriQ∑i=1nrixi=∑i=1nri2∑i=1nriQ(xi)in Banach modules over a unital C*-algebra, where n>1 is a positive integer and {ri∈(0,∞)|i=1,…,n} is arbitrary given.