文章基本信息

标题：The fixed point alternative and Hyers-Ulam stability of generalized additive set-valued functional equations
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作者：Sun Young Jang
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：127
DOI：10.1186/1687-1847-2014-127
语种：English
出版社：Hindawi Publishing Corporation
摘要：We define generalized additive set-valued functional equations, which are related with the following generalized additive functional equations: f ( x 1 + ⋯ + x l ) = ( l − 1 ) f ( x 1 + ⋯ + x l − 1 l − 1 ) + f ( x l ) , f ( x 1 + ⋯ + x l − 1 l − 1 + x l ) + f ( x 1 + ⋯ + x l − 2 + x l l − 1 + x l − 1 ) + ⋯ + f ( x 2 + ⋯ + x l l − 1 + x 1 ) = 2 [ f ( x 1 ) + f ( x 2 ) + ⋯ + f ( x l ) ] for a fixed integer l with l > 1 , and they prove the Hyers-Ulam stability of the generalized additive set-valued functional equations by using the fixed point method. MSC: 39B52, 54C60, 91B44.
关键词：Hyers-Ulam stability ; generalized additive set-valued functional equation ; closed and convex set ; cone