Stability of the Pexiderized Lobacevski equation (Q642772)

Summary: The aim of this paper is to investigate the solution and the superstability of the Pexiderized Lobachevski equation \(f((x + y)/2)^2 = g(x)h(y)\), where \(f, g, h : G^2 \to \mathbb C\) are unknown functions on an abelian semigroup \((G, +)\). The obtained result is a generalization of \textit{P. Găvruţă}\,'s result in 1994 [J. Math. Anal. Appl. 184, No. 3, 431--436 (1994; Zbl 0818.46043)] and \textit{G. H. Kim}'s result in 2010 [J. Nonlinear Sci. Appl. 4, No. 1, 11--18 (2011; Zbl 1206.39024)].