Stability for a family of equations generalizing the equation of p-Wright affine functions

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• 作者：Janusz Brzdȩk^a ; ^{jbrzdek@ap.krakow.pl" class="auth_mail" title="E-mail the corresponding author} ; Liviu Cădariu ; ^b ; ^{liviu.cadariu-brailoiu@upt.ro" class="auth_mail" title="E-mail the corresponding author} ; ^{lcadariu@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Generalized Hyers&ndash ; Ulam stability ; p-Wright affine function ; Hyperstability ; Fixed points
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：5 March 2016
• 年：2016
• 卷：276
• 期：Complete
• 页码：158-171
• 全文大小：378 K

文摘

We prove some general stability results for a family of equations, which generalizes the equation of p-Wright affine functions. In this way we obtain some hyperstability properties for those equations, as well. We also provide some applications of those outcomes in proving inequalities characterizing the inner product spaces and stability of *-homomorphisms of C^*-algebras. The main tool in the proofs is a fixed point result in Brzdȩk, Chudziak, Páles (2011).