Differentiable solutions of equations involving iterated functional series.
Song, Wei (2008)
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Song, Wei (2008)
Abstract and Applied Analysis
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Katarzyna Sajbura (2005)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Our aim is to study continuous solutions φ of the classical linear iterative equation φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y), where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.
Song, Wei, Chen, Sheng, Yin, Xunbo (2010)
Discrete Dynamics in Nature and Society
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An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations...
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Annales Polonici Mathematici
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