On the Ulam stability of Jensen and Jensen type mappings on restricted domains

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• 作者：Rassias ; John Michael ; Rassias ; Matina John
• 关键词：Ulam stability problem ; Hyers&ndash ; Ulam stability ; Ulam stability ; Approximately odd mapping ; Additive of the first form ; Additive of the second form ; Jensen equation ; Jensen type equation ; Restricted domain
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2003
• 出版时间：May 15, 2003
• 年：2003
• 卷：281
• 期：2
• 页码：516-524
• 全文大小：85.0 K

文摘

In 1941 Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 Bourgin was the second author to treat this problem for additive mappings. In 1982–1998 Rassias established the Hyers–Ulam stability of linear and nonlinear mappings. In 1983 Skof was the first author to solve the same problem on a restricted domain. In 1998 Jung investigated the Hyers–Ulam stability of more general mappings on restricted domains. In this paper we introduce additive mappings of two forms: of “Jensen” and “Jensen type,” and achieve the Ulam stability of these mappings on restricted domains. Finally, we apply our results to the asymptotic behavior of the functional equations of these types.