A remark on <it>k</it>th-order linear functional equations with constant coefficients

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.