A Class of Continuous Solutions of a Fourth Order Polynomial-like Iterative Equation

Main Article Content

Supharerg Thangroongvongthana*
Vichian Laohakosol
Sukrawan Mavecha

Abstract

Using the so-called characteristic method, continuous solutions of the fourth order polynomial-like iterative equation


gif.latex?f^{4}(x)+a_{3}f^{3}(x)+a_{2}f^{2}(x)+a_{1}f(x)+a_{0}x&space;=&space;0


were determined subject to certain natural conditions on its characteristic roots. The result so obtained complements earlier work in the cases of second and third order equations.


 
Keywords: polynomial-like iterative equation; continuous solution; characteristic root    

Corresponding author: Tel.: +66 838214391


                                           E-mail: [email protected]

Article Details

Section
Original Research Articles

References

Matkowski, J. and Weinian, Z., 1997. Method of characteristic for functional equations in polynomial form. Acta Mathematica Sinica, 13(3), 421-432.

Matkowski, J. and Zhang, W., 2000. On linear dependence of iterates. Journal of Applied Analysis, 6(1), 149-157.

Yang, D. and Zhang, W., 2004. Characteristic solutions of polynomial-like iterative equations. Aequationes Mathematicae, 67, 80-105.

Zhang, P. and Gong, X., 2014. Continuous solutions of 3rd-order iterative equation of linear dependence. Advances in Difference Equations, 2014, 318, https://doi.org/10.1186/1687-1847-2014-318

Nabeya, S., 1974. On the functional equation f(p+qx+rf(x)) = a+bx+cf(x) Aequationes Mathematicae, 11, 199-211.

Kuczma, M., 1968. Functional Equations in a Single Varible (Monografic Matematyczne). Warszwa : PWN-Polish Scientific Publishers.