tailieunhanh - Báo cáo hóa học: " Research Article Investigation of the Stability via Shadowing Property"

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: Research Article Investigation of the Stability via Shadowing Property | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 156167 12 pages doi 2009 156167 Research Article Investigation of the Stability via Shadowing Property Sang-Hyuk Lee 1 Heejeong Koh 2 and Se-Hyun Ku3 1 School of Mecatronics Engineering Changwon National University Sarim 9 Changwon Gyeongnam 641-773 South Korea 2 Department of Mathematics Education College of Education Dankook University 126 Jukjeon Suji Yongin Gyeongi 448-701 South Korea 3 Department of Mathematics Chungnam National University 79 Daehangno Yuseong-Gu Daejeon 305-764 South Korea Correspondence should be addressed to Se-Hyun Ku shku@ Received 25 November 2008 Revised 16 February 2009 Accepted 19 May 2009 Recommended by Ulrich Abel The shadowing property is to find an exact solution to an iterated map that remains close to an approximate solution. In this article using shadowing property we show the stability of the following equation in normed group 4n-2Cn 2-1r2f ifj itxj r n Zike 0 1 su ik n 2 rf V 1 -V Xi rf 4n n-2Cn 2-1 i 1f xi where n 2 r e R r2 n and f is a mapping. And we prove that the even mapping which satisfies the above equation is quadratic and also the Hyers-Ulam stability of the functional equation in Banach spaces. Copyright 2009 Sang-Hyuk Lee et al. 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 notion of pseudo-orbits very often appears in several areas of the dynamical systems. A pseudo-orbit is generally produced by numerical simulations of dynamical systems. One may consider a natural question which asks whether or not this predicted behavior is close to the real behavior of system. The above property is called the shadowing property or pseudo-orbit tracing property . The shadowing property is an important feature of stable dynamical .