IJPAM: Volume 94, No. 1 (2014)

ON DERIVATION OF RATIONAL SOLUTIONS
OF BABBAGE'S FUNCTIONAL EQUATION

Ampon Dhamacharoen$^1$, Porntip Kasempin$^2$
$^{1,2}$Department of Mathematics
Burapha University
Bangsaen, Chonburi, 20131, THAILAND


Abstract. This paper investigates the functional $n^{th}$ root of the identity function in the rational form $f(x)$ $=$ $\dfrac{ax+b}{cx+d}$. The formula is analyzed via linear transformation in order to obtain the conditions for a, b, c and d. Some examples in linear rational form or in other forms are provided. The rational form of quadratic functions is also discussed.

Received: August 19, 2013

AMS Subject Classification: 39B72, 39B12, 26C15, 39B72, 40C05

Key Words and Phrases: functional root, Babbage's equation, rational form, functional equation, matrix representation

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DOI: 10.12732/ijpam.v94i1.2 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 94
Issue: 1
Pages: 9 - 20

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).