On the completeness of normed spaces (Q979163)

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scientific article; zbMATH DE number 5726674
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On the completeness of normed spaces
scientific article; zbMATH DE number 5726674

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    On the completeness of normed spaces (English)
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    25 June 2010
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    The main problem being solved in the paper under review was already proposed by the reviewer in the Conference on Inequalities and Applications, which was held in Noszvaj-Hungary in 2007 [see Problem 3, page xlii, \textit{C. Bandle, A. Gilányi, L. Losonczi, Z. Páles} and \textit{M. Plum} (eds.), Inequalities and applications. International Series of Numerical Mathematics 157. Basel: Birkhäuser (2009; Zbl 1148.26004)]. At the same conference, it was solved in an elegant and short way. This solution, in a general form, can be found in \textit{R. Ger}, \textit{A. Gilanyi} and \textit{P. Volkmann} [Ann. Math. Silesianae 25 (2009), 112--113 (2010)].
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    Hyers-Ulam stability
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    quadratic functional equation
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    completeness
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    normed spaces
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