Generalized Stability of Euler-Lagrange Quadratic Functional Equation in Random Normed Spaces under Arbitrary $t$-Norms

Z. Baderi, R. Saadati

Abstract

he main goal of this paper is the investigation of the generalized Hyers-Ulam stability theorem of thefollowing Euler-Lagrange type quadratic functional equation\begin{eqnarray*}f(ax+by) + a f(x-by)=(a+1)b^2 f(y)+a(a+1)f(x)\end{eqnarray*}in random normed spaces under arbitrary t-norms, where $a,b$ are fixed integer numbers such that   $a\neq -1,0,1$ and  $b\neq$0.