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

Abstract

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

$f^{4}(x)+a_{3}f^{3}(x)+a_{2}f^{2}(x)+a_{1}f(x)+a_{0}x = 0$

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: supharerg@gmail.com

How to Cite

Citation Format

Thangroongvongthana*, S. undefined. ., Laohakosol, V. undefined. ., & Mavecha, S. undefined. . (2021). A Class of Continuous Solutions of a Fourth Order Polynomial-like Iterative Equation. CURRENT APPLIED SCIENCE AND TECHNOLOGY, 495-523.

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.

Author Information

Supharerg Thangroongvongthana*

Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

Vichian Laohakosol

Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok, Thailand

Sukrawan Mavecha

Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

About this Article

Journal

Vol. 21 No. 3 (2021)

Type of Manuscript

Original Research Article

Keywords

polynomial-like iterative equation; continuous solution; characteristic root

Published

25 January 2021

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

Abstract

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

How to Cite

References

Author Information

Supharerg Thangroongvongthana*

Vichian Laohakosol

Sukrawan Mavecha

About this Article

Journal

Type of Manuscript

Keywords

Published

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