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

Annales Polonici Mathematici (2000)

- Volume: 73, Issue: 1, page 29-36
- ISSN: 0066-2216

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topZhang, Weinian, and Baker, John. "Continuous solutions of a polynomial-like iterative equation with variable coefficients." Annales Polonici Mathematici 73.1 (2000): 29-36. <http://eudml.org/doc/262652>.

@article{Zhang2000,

abstract = {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.},

author = {Zhang, Weinian, Baker, John},

journal = {Annales Polonici Mathematici},

keywords = {functional equation; fixed point theorem; iterative root; continuous solutions; variable coefficients; stability; iterative functional equation},

language = {eng},

number = {1},

pages = {29-36},

title = {Continuous solutions of a polynomial-like iterative equation with variable coefficients},

url = {http://eudml.org/doc/262652},

volume = {73},

year = {2000},

}

TY - JOUR

AU - Zhang, Weinian

AU - Baker, John

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

JO - Annales Polonici Mathematici

PY - 2000

VL - 73

IS - 1

SP - 29

EP - 36

AB - 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.

LA - eng

KW - functional equation; fixed point theorem; iterative root; continuous solutions; variable coefficients; stability; iterative functional equation

UR - http://eudml.org/doc/262652

ER -

## References

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- [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. Zbl0518.39005
- [7] S. Nabeya, On the function equation f(p + qx + rf(x)) = a + bx + cf(x), Aequationes Math. 11 (1974), 199-211. Zbl0289.39003
- [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). Zbl0529.39006
- [9] W. N. Zhang, Discussion on the iterated equation ${\sum}_{i=1}^{n}{\lambda}_{i}{f}^{i}\left(x\right)=F\left(x\right)$, Chinese Sci. Bull. 32 (1987), 1444-1451. Zbl0639.39006
- [10] W. N. Zhang, Stability of the solution of the iterated equation ${\sum}_{i=1}^{n}{\lambda}_{i}{f}^{i}\left(x\right)=F\left(x\right)$, Acta Math. Sci. 8 (1988), 421-424. Zbl0664.39004
- [11] W. N. Zhang, Discussion on the differentiable solutions of the iterated equation ${\sum}_{i=1}^{n}{\lambda}_{i}{f}^{i}\left(x\right)=F\left(x\right)$, Nonlinear Anal. 15 (1990), 387-398.

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