Korean J. Math. Vol. 23 No. 3 (2015) pp.393-399
DOI: https://doi.org/10.11568/kjm.2015.23.3.393

Approximate additive mappings in $2$-Banach spaces and related topics: revisited

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Published: Sep 30, 2015
Keywords:
Hyers-Ulam stability, Linear 2-normed space, Additive mapping, Jensen mapping, Quadratic mapping.
Mathematics Subject Classification:
46B99, 39B82, 39B52.

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Sungsik Yun
Department of Financial Mathematics Hanshin University Osan 447-791, Korea

Abstract

W. Park [J. Math. Anal. Appl. 376 (2011) 193–202] proved the Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. But there are serious problems in the control functions given in all theorems of the paper.

In this paper, we correct the statements of these results and prove the corrected theorems.

Moreover, we prove the superstability of the Cauchy functional equation, the Jensen functional equation and the quadratic func- tional equation in 2-Banach spaces under the original given condi- tions.



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