Continuous solutions of a polynomial-like iterative equation with variable coefficients

• Autorzy: Weinian Zhang , John A. Baker
• Języki publikacji: EN

Abstrakty

EN

Using the fixed point theorems of Banach and Schauder we discuss the existence, uniqueness and stability of continuous solutions of a polynomial-like iterative equation with variable coefficients.

Słowa kluczowe

EN

functional equation   fixed point theorem   iterative root  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 73
• Numer: 1
• Strony: 29-36

Daty

wydano

2000

otrzymano

1998-08-18

Twórcy

autor

Weinian Zhang

• Department of Mathematics Sichuan Union University Chengdu 610064 P.R. China

autor

John A. Baker

• Department of Pure Mathematics University of Waterloo Waterloo, Ontario, Canada N2L 3G1

Bibliografia

• [1] N. H. Abel, Oeuvres complètes, Vol. II, Christiania, 1981, 36-39.
• [2] J. G. Dhombres, Itération linéaire d'ordre deux, Publ. Math. Debrecen 24 (1977), 277-287.
• [3] J. M. Dubbey, The Mathematical Work of Charles Babbage, Cambridge Univ. Press, 1978.
• [4] M. Kuczma, Functional Equations in a Single Variable, Monograf. Mat. 46, PWN, Warszawa, 1968.
• [5] M. Kuczma, B. Choczewski, and R. Ger, Iterative Functional Equations, Encyclopedia Math. Appl. 32, Cambridge Univ. Press, 1990.
• [6] A. Mukherjea and J. S. Ratti, On a functional equation involving iterates of a bijection on the unit interval, Nonlinear Anal. 7, (1983), 899-908.
• [7] S. Nabeya, On the function equation f(p + qx + rf(x)) = a + bx + cf(x), Aequationes Math. 11 (1974), 199-211.
• [8] J. Z. Zhang and L. Yang, Discussion on iterative roots of continuous and piecewise monotone functions, Acta Math. Sinica 26 (1983), 398-412 (in Chinese).
• [9] W. N. Zhang, Discussion on the iterated equation $∑^n_{i=1} λ_i f^i(x) = F(x)$, Chinese Sci. Bull. 32 (1987), 1444-1451.
• [10] W. N. Zhang, Stability of the solution of the iterated equation $ ∑^n_{i=1} λ_i f^i(x) = F(x)$, Acta Math. Sci. 8 (1988), 421-424.
• [11] W. N. Zhang, Discussion on the differentiable solutions of the iterated equation $∑^n_{i=1} λ_i f^i(x) = F(x)$, Nonlinear Anal. 15 (1990), 387-398.