A remark on k th-order linear functional equations with constant coefficients
© Jitka Laitochová 2006
Received: 30 January 2006
Accepted: 18 May 2006
Published: 14 September 2006
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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