Analytic solutions of a polynomial-like iterative functional equation

• Autorzy: Si J. , Wang X.
• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with a polynomial-like iterative functional equation lambda1f(z) + lambda2f(2)(z) + .. . . + lambdamf[m](z) = F(z), where f(z) is an unknown function, F(z) is a given function, f[i]l denotes the i-th iterate of f, and lambda1, lambda2, . . .,lambdam are complex constants. By constructing a convergent power series solution phi(z) of an auxiliary equation of the form lambda1alpha(alphaz)+lambda2phi(alpha2z)+.....+lambdamphi(alphamz)=F(phi(z)), analytic solutions of the form phi(alphaphi-1(z)) for the original iterative functional equation are obtained.

Słowa kluczowe

EN

iterative functional equation; analytic solution

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 1999
• Tom: Vol. 32, nr 1
• Strony: 95--103
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Si J.

• Department of Mathematica Binzhou Normal College Binzhou, Shandong, 256604 P. R. China

autor

Wang X.

• Department of Mathematica Binzhou Normal College Binzhou, Shandong, 256604 P. R. China

Bibliografia

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• [6] W. Zhang, Discussion on the differentiable solutions of the iterated equation [formula] Nonlinear Anal. 15 (1990), 387-398.
• [7] Si. Jian-Guo, On the monotonie continuous solutions of some iterated equation, Demonstratio Math. 29 (1996), 543-547.
• [8] J. Matkowski and W. Zhang, Method of characteristic for functional equation in polynomial form, Acta Math. Sin. New Series, 13 (1997), 421-432.