Additive functional equation and inequality are stable in Banach space and its applications

M. Arunkumara,*  and P. Agilanb

Additive functional equation and inequality are stable in Banach space and its applications

Authors :

M. Arunkumar^a,* and P. Agilan^b

Author Address :

^aDepartment of Mathematics, Government Arts College, Tiruvannamalai - 606 603, Tamil Nadu, India.
^bDepartment of Mathematics, S.K.P. Engineering College, Tiruvannamalai - 606 611, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper, the authors established the solution of the additive functional equation and inequality
\begin{align*}
f(x)+f(y+z)-f(x+y)=f(z)
\end{align*}
and
\begin{align*}
||f(x)+f(y+z)-f(x+y)|| \leq ||f(z)||.
\end{align*}
We also prove that the above functional equation and inequality are stable in Banach space in the sense of Ulam, Hyers, Rassias. An application of this functional equation is also studied.

Keywords :

Additive functional equations, generalized Hyers - Ulam - Rassias stability.

DOI :

Article Info :

Received : September 29, 2012; Accepted : November 03, 2012.