Closed form solutions of iterative functional differential equations.
Li, Wenrong, Cheng, Sui Sun, Lu, Tzon Tzer (2001)
Applied Mathematics E-Notes [electronic only]
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Li, Wenrong, Cheng, Sui Sun, Lu, Tzon Tzer (2001)
Applied Mathematics E-Notes [electronic only]
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Bing Xu (2004)
Annales Polonici Mathematici
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Analytic solutions of polynomial-like iterative functional equations with variable coefficients are discussed in the complex field ℂ by reducing to an auxiliary equation and by applying known results for systems of nonlinear functional equations of finite orders.
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 (2008)
Abstract and Applied Analysis
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B. Jovanović (1972)
Matematički Vesnik
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W. Solak (1971)
Annales Polonici Mathematici
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Z. Kowalski (1963)
Annales Polonici Mathematici
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Detlef Gronau (1982)
Aequationes mathematicae
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Weinian Zhang (1997)
Annales Polonici Mathematici
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The concept of characteristic interval for piecewise monotone functions is introduced and used in the study of their iterative roots on a closed interval.
B. Jovanović (1972)
Matematički Vesnik
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Solarz, Paweł (2002)
Mathematica Pannonica
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Jean-Claude Ndogmo, Fazal Mahomed (2014)
Open Mathematics
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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...
Z. Krzeszowiak-Dybiec (1980)
Annales Polonici Mathematici
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Z. Krzeszowiak-Dybiec (1980)
Annales Polonici Mathematici
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Beata Strycharz-Szemberg, Tomasz Szemberg (2011)
Open Mathematics
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We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.