tailieunhanh - Báo cáo hóa học: " Superstability of generalized cauchy functional equations"

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: Superstability of generalized cauchy functional equations | Lee and Chung Advances in Difference Equations 2011 2011 23 http content 2011 1 23 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Superstability of generalized cauchy functional equations Young-Su Lee1 and Soon-Yeong Chung2 Correspondence masuri@sogang. department of Mathematics Sogang University Seoul 121-741 Republic of Korea Full list of author information is available at the end of the article Abstract In this paper we consider the stability of generalized Cauchy functional equations such as f x y f xMy f y z f xy f x g y f y . Especially interesting is that such equations have the Hyers-Ulam stability or superstability whether g is identically one or not. 2000 Mathematics Subject Classification 39B52 39B82. Keywords Cauchy functional equation stability superstability V J 1. Introduction The most famous functional equations are the following Cauchy functional equations f x y f x f y 1 1 f x y f x f y f xy f x f y 1-3 f xy f x f y . 1-4 Usually the solutions of - are called additive exponential logarithmic and multiplicative respectively. Many authors have been interested in the general solutions and the stability problems of - see 1-5 . The stability problems of functional equations go back to 1940 when Ulam 6 proposed the following question Letfbe a mapping from a group G to a metric group G2 with metric d f such that d f xy f x f y e. Then does there exist a group homomorphism L G G2 and tf 0 such that d f x L x se for all X e G1 SpringerOpen0 2011 Lee and Chung licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http licenses by which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Lee and Chung Advances in Difference Equations 2011 2011 23 http content 2011 1 23 Page