Advances in Difference Equations
Volume 2006 (2006), Article ID 72615, 8 pages
doi:10.1155/ADE/2006/72615
A remark on kth-order linear functional equations with constant coefficients
Mathematical Department, Faculty of Education, Palacký University, Žižkovo náměsti 5, Olomouc 77140, Czech Republic
Received 30 January 2006; Accepted 18 May 2006
Copyright © 2006 Jitka Laitochová. 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.
Abstract
Abel functional equations are associated to a linear
homogeneous functional equation with constant coefficients. The
work uses the space S of continuous strictly monotonic
functions. Generalized terms are used, because of the space S, like composite function, iterates of a function, Abel functional
equation, and linear homogeneous functional equation in S with constant coefficients. The classical theory of linear homogeneous
functional and difference equations is obtained as a special case
of the theory in space S. Equivalence of points and orbits of a
point are introduced to show the connection between the linear
functional and the linear difference equations in S. Asymptotic behavior at infinity is studied for a solution of the linear
functional equation.