IJPAM: Volume 74, No. 2 (2012)

STABILITY FOR MIXED TYPE OF ADDITIVE AND
QUADRATIC FUNCTIONAL EQUATION IN RANDOM
NORMED SPACES VIA FIXED POINT METHOD

Yang-Hi Lee$^1$, Won-Gil Park$^2$, Ick-Soon Chang$^3$
$^1$Department of Mathematics Education
Gongju National University of Education
Gongju 314-711, REPUBLIC OF KOREA
$^{2,3}$Department of Mathematics Education
Mokwon University
Daejeon, 302-729, REPUBLIC OF KOREA


Abstract. In this paper, we prove the stability in random normed space via fixed point method for the following additive and quadratic type functional equation
\begin{align}
f(x+ y)- f(-x- y)-f(x )+ f(- x)-4f(y)+f(2y) =0.
\end{align}


Received: December 13, 2011

AMS Subject Classification: 39B52, 39B72, 39B82, 43A22,46S40, 47B47

Key Words and Phrases: stability, additive mapping, cubic mapping, random normed space, Ulam-Gavruta-Rassias (or UGR), product of different powers of norms, JMRassias (or JMR), mixed product-sum of powers of norms

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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: 74
Issue: 2