Abstract and Applied Analysis
Volume 2009 (2009), Article ID 907167, 11 pages
doi:10.1155/2009/907167
The stability of a quadratic functional equation with the fixed point alternative
Choonkil Park1
and Ji-Hye Kim2
1Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea
2Department of Mathematics, Hanyang University, Seoul 133-791, South Korea
Abstract
Lee, An and Park introduced the quadratic functional equation f(2x+y)+f(2x−y)=8f(x)+2f(y) and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.