IJPAM: Volume 77, No. 3 (2012)

STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY
WITH THE FIXED POINT ALTERNATIVE

Won-Gil Park$^1$, Mi Hyun Han$^2$
$^1$Department of Mathematics Education
College of Education
Mokwon University
Daejeon, 302-729, REPUBLIC OF KOREA
$^2$Departament of Mathematics
Chungnam National University
220, Yuseong-Gu, Daejeon, 305-764, REPUBLIC OF KOREA


Abstract. In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality
\begin{align*}
\b\Vert f(x)+2f(y)+2f(z)\b\Vert&\le\b\Vert f(x)+f(2y+2z)\b\Vert
\end{align*}
by using a fixed point method in Banach spaces.

Received: March 7, 2012

AMS Subject Classification: 39B82, 46Bxx

Key Words and Phrases: additive functional inequality, Banach space, fixed point alternative

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 3