Stability of the Pexiderized Lobacevski Equation

Abstract

The aim of this paper is to investigate the solution and the superstability of the Pexiderized Lobacevski equation $f{\left(\right(x+y)/2)}^2=g\left(x\right)h\left(y\right)$, where $f$, $g$, $h:G^2\to C$ are unknown functions on an Abelian semigroup $(G,+)$. The obtained result is a generalization of Gavruta's result in 1994 and Kim's result in 2010.