Advances in Difference Equations
Volume 2006 (2006), Article ID 72615, 8 pages

A remark on kth-order linear functional equations with constant coefficients

Jitka Laitochová

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.


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.