Open Access

A remark on k th-order linear functional equations with constant coefficients

Advances in Difference Equations20062006:072615

https://doi.org/10.1155/ADE/2006/72615

Received: 30 January 2006

Accepted: 18 May 2006

Published: 14 September 2006

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.

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Authors’ Affiliations

(1)
Mathematical Department, Faculty of Education, Palacký University

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Copyright

© Jitka Laitochová 2006

This article is published under license to BioMed Central Ltd. 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.