Several stability problems of a quadratic functional equation
Commun. Korean Math. Soc. 2011 Vol. 26, No. 1, 99-113
Printed March 1, 2011
In Goo Cho and Hee Jeong Koh
University of Incheon, Dankook University
Abstract : 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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