Approximate Solutions of the Generalized Golab-schinzel Equation

play a significant role in the theory of functional equations. Some information on the applications of (1.1) and (1.2) in the determination of substructures of algebraical structures, in the theory of geometric objects and classification of near-rings and quasialgebras, can be found, for example, in [1–5] and in the recent survey paper [6]. At the 38th International Symposium on Functional Equations (2000, Noszvaj, Hungary), R. Ger raised, among others, the problem of Hyers-Ulam stability for the Goła̧bSchinzel-type functional equations (see [6, page 21] and [12]). In the case of (1.1), this problem has been studied in [7, 8, 10]. Recently, in [9] it has been proved that (1.2) is superstable in the class of continuous functions f :R→R. In the present paper, we deal with the stability problem for (1.2) in the case where f is defined on a linear space over the field K of real or complex numbers and takes its values in K . Throughout the paper, N, Z, and R stand for the sets of all positive integers, integers, and real numbers, respectively.