Fixed points and stability of lcosic functional equation in quasi- $\beta$-normed spaces

V. Govindhan; S. Murthy; G. Gokila

doi:10.26637/MJM0601/0030

Abstract

In this paper, we introduce the following icosic functional equation. This pioneering icosic functional equation
$$
\begin{gathered}
f(x+10 y)-20 f(x+9 y)+190 f(x+8 y)-1140 f(x+7 y)+4845 f(x+6 y)-15504 f(x+5 y) \\
+38760 f(x+4 y)-77520 f(x+3 y)+125970 f(x+2 y)-167960 f(x+y)+184756 f(x) \\
-167960 f(x-y)+125970 f(x-2 y)-77520 f(x-3 y)+38760 f(x-4 y)-15504 f(x-5 y) \\
+4845 f(x-6 y)-1140 f(x-7 y)+190 f(x-8 y)-20 f(x-9 y)+f(x-10 y)=20 ! f(y),
\end{gathered}
$$
where $20 !=2.432902008 \times 10^8$, 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- $\beta$-normed space.

Keywords:

Icosic functional equation, \text { Quasi } \beta \text {-normed space }, Fixed point

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

V. Govindhan Department of Mathematics, Sri Vidya Mandir Arts and Science College, Katteri, Tamilnadu, India.
S. Murthy Department of Mathematics, Government Arts and Science College (For Men), Krishnagiri - 635 001, Tamil Nadu, India.
G. Gokila Department of Mathematics, Government Arts and Science College (For Men), Krishnagiri - 635 001, Tamil Nadu, India.

Pages: 261-275
Date Published: 01-01-2018
Vol. 6 No. 01 (2018): Malaya Journal of Matematik (MJM)

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