tailieunhanh - Báo cáo hóa học: "APPROXIMATE SOLUTIONS OF THE GENERALIZED GOŁAB-SCHINZEL EQUATION "

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: APPROXIMATE SOLUTIONS OF THE GENERALIZED GOŁAB-SCHINZEL EQUATION | APPROXIMATE SOLUTIONS OF THE GENERALIZED GOLAB-SCHINZEL EQUATION JACEK CHUDZIAK Received 24 March 2006 Revised 12 July 2006 Accepted 28 July 2006 Motivated by the problem of R. Ger we show that the generalized Goỉạb-Schinzel equation is superstable in the class of functions hemicontinuous at the origin. As a consequence we obtain the form of approximate solutions of that equation. Copyright 2006 Jacek Chudziak. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction The Golab-Schinzel equation f x f x y f x f y and its generalized version f x f x ky Xf x f y play a significant role in the theory of functional equations. Some information on the applications of and 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 Golab-Schinzel-type functional equations see 6 page 21 and 12 . In the case of this problem has been studied in 7 8 10 . Recently in 9 it has been proved that is superstable in the class of continuous functions f R R. In the present paper we deal with the stability problem for 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. Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2006 Article ID 89402 Pages 1-8 DOI JIA 2006 89402 2 Approximate solutions of the Goỉạb-Schinzel equation 2. Results From now on we assume that K is a field of