IJPAM: Volume 77, No. 2 (2012)

APPROXIMATE ADDITIVE MAPPINGS RELATED TO
A CAUCHY ADDITIVE FUNCTIONAL INEQUALITY

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


Abstract. In this paper, we prove the generalized Hyers-Ulam stability of the following additive functional inequality

\begin{displaymath}\b\Vert f(x)+f(y)+f(-z)\b\Vert\le\b\Vert f(x+y)-f(z)\b\Vert\end{displaymath}

in Banach spaces. We investigate the stability of the above functional inequality in non-Archimedean Banach spaces.

Received: January 20, 2012

AMS Subject Classification: 39B82, 46Bxx

Key Words and Phrases: additive functional inequality, Banach space, non-Archimedean Banach space

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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: 2