期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 62, 期 6, 页码 2648-2657出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2011.08.007
关键词
Linear equation; Hyers-Ulam stability; Nonstability; Characteristic root; Normed space
We provide a complete solution of the problem of Hyers-Ulam stability for a large class of higher order linear functional equations in single variable, with constant coefficients. We obtain this by showing that such an equation is nonstable in the case where at least one of the roots of the characteristic equation is of module 1. Our results are related to the notions of shadowing (in dynamical systems and computer science) and controlled chaos. They also correspond to some earlier results on approximate solutions of functional equations in single variable. (C) 2011 Elsevier Ltd. All rights reserved.
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