Commun. Korean Math. Soc. 2011; 26(1): 99-113
Printed March 1, 2011
https://doi.org/10.4134/CKMS.2011.26.1.99
Copyright © The Korean Mathematical Society.
In Goo Cho and Hee Jeong Koh
University of Incheon, Dankook University
In this paper, we investigate the stability using shadowing property in Abelian metric group and the generalized Hyers-Ulam-Rassias stability in Banach spaces of a quadratic functional equation, \begin{eqnarray*} &&f(x_1+x_2+x_3+x_4)+f(-x_1+x_2-x_3+x_4) \\ &&+f(-x_1+x_2+x_3)+f(-x_2+x_3+x_4)+f(-x_3+x_4+x_1)\\ &&+f(-x_4+x_1+x_2)=5\sum^4_{i=1}f(x_i). \end{eqnarray*} Also, we study the stability using the alternative fixed point theory of the functional equation in Banach spaces.
Keywords: shadowing property-stability, generalized Hyers-Ulam stability, quadratic mapping
MSC numbers: 39B52
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2012; 27(1): 149-158
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