Approximately Quadratic Mappings on Restricted Domains

Details Approximately Quadratic Mappings on Restricted Domains Approximately Quadratic Mappings on Restricted Domains

2011-01-06

arxiv.org/abs/1101.1171v1

J. Inequalities and Applications, Volume 2010, Article ID 503458

Mathematics

Functional Analysis

9 pages

Scientific paper

10.1155/2010/503458

In this paper, we introduce a generalized quadratic functional equation $f(rx + sy) = rf(x) + sf(y) - rsf(x - y)$ where $r, s$ are nonzero real numbers with $r + s = 1.$ We show that this functional equation is quadratic if $r, s$ are rational numbers. We also investigate its stability problem on restricted domains. These results are applied to study of an asymptotic behavior of these generalized quadratic mappings.

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