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

Advances in Difference Equations volume 2006, Article number: 072615 (2006) Cite this article

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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  1. Mathematical Department, Faculty of Education, Palacký University, Žižkovo náměsti 5, Olomouc, 77140, Czech Republic

    Jitka Laitochová

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  1. Jitka Laitochová
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Correspondence to Jitka Laitochová.

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Laitochová, J. A remark on k th-order linear functional equations with constant coefficients. Adv Differ Equ 2006, 072615 (2006). https://doi.org/10.1155/ADE/2006/72615

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