On the Ulam stability of mixed type mappings on restricted domains

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• 作者：Rassias ; John Michael
• 关键词：Ulam stability problem ; Hyers&ndash ; Ulam stability ; Approximately even (or odd) mapping ; Restricted domain
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2002
• 出版时间：December 15, 2002
• 年：2002
• 卷：276
• 期：2
• 页码：747-762
• 全文大小：120 K

文摘

In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982–1998 we established the Hyers–Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1983 F. Skof was the first author to solve the Ulam problem for additive mappings on a restricted domain. In 1998 S.M. Jung investigated the Hyers–Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve the bounds and thus the results obtained by S.M. Jung, in 1998. Besides we establish the Ulam stability of mixed type mappings on restricted domains. Finally, we apply our recent results to the asymptotic behavior of functional equations of different types.