Fixed points and stability of Icosic functional equation in quasi-$eta$-normed spaces

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Authors :

V. Govindhan 1*, S. Murthy2 and G. Kokila 3

Author Address :

1Department of Mathematics, Sri Vidya Mandir Arts and Science College, Katteri, Tamilnadu, India.

2,3Department of Mathematics, Government Arts and Science College (For Men), Krishnagiri - 635 001, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper, we introduce the following icosic functional equation. This pioneering icosic functional equation
$$ f(x+10y) - 20 f(x + 9y) + 190 f(x + 8y) - 1140 f(x+7y) + 4845 f(x+6y) - 15504 f(x+5y) $$
$$ + 38760 f(x+4y) - 77520 f(x+3y) + 125970 f(x+2y) - 167960 f(x+y) + 184756 f(x) $$
$$ - 167960 f(x-y) + 125970 f(x-2y) - 77520 f(x-3y) + 38760 f(x-4y) - 15504 f(x-5y) $$
$$ + 4845 f(x - 6y) - 1140 f(x-7y) + 190 f(x-8y) - 20 f(x - 9y) + f(x - 10y) = 20 ! f(y) , $$
where $ 20 ! = 2. 432902008 imes 10^8 $, is said to be icosic functional equation. Since the functional equation $f(x) = x^{20}$ is the solution. In this paper, we present the general solutions of the said icosic functional equation. We also prove the stability of the icosic functional equation in a quasi-$eta$-normed space.

Keywords :

Icostic functional equation, Quasi $eta$-normed space, Fixed point.

DOI :

10.26637/MJM0601/0030

Article Info :

Received : November 26, 2017; Accepted : December 27, 2017.