Asymptotic stability of the Cauchy and Jensen functional equations

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• 作者：A. Bahyrycz ; Zs. Páles ; M. Piszczek
• 关键词：Mathematics Subject Classification39B82
• 刊名：Acta Mathematica Hungarica
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：150
• 期：1
• 页码：131-141
• 全文大小：710 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Sciences
  Mathematics
  
• 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
• ISSN：1588-2632
• 卷排序：150

文摘

The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid everywhere with a new error term which is a constant multiple of the original error term. As consequences, we also obtain results of hyperstability character for these two functional equations.