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

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1. [1] N. H. Abel, Oeuvres complètes, Vol. II, Christiania, 1981, 36-39. 
2. [2] J. G. Dhombres, Itération linéaire d'ordre deux, Publ. Math. Debrecen 24 (1977), 277-287. Zbl0398.39006
3. [3] J. M. Dubbey, The Mathematical Work of Charles Babbage, Cambridge Univ. Press, 1978. Zbl0376.01002
4. [4] M. Kuczma, Functional Equations in a Single Variable, Monograf. Mat. 46, PWN, Warszawa, 1968. 
5. [5] M. Kuczma, B. Choczewski, and R. Ger, Iterative Functional Equations, Encyclopedia Math. Appl. 32, Cambridge Univ. Press, 1990. Zbl0703.39005
6. [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. [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. [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. [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. [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. [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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