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http://dx.doi.org/10.11568/kjm.2015.23.3.393

APPROXIMATE ADDITIVE MAPPINGS IN 2-BANACH SPACES AND RELATED TOPICS: REVISITED  

YUN, SUNGSIK (Department of Financial Mathematics Hanshin University)
Publication Information
Korean Journal of Mathematics / v.23, no.3, 2015 , pp. 393-399 More about this Journal
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 functional equation in 2-Banach spaces under the original given conditions.
Keywords
Hyers-Ulam stability; Linear 2-normed space; Additive mapping; Jensen mapping; Quadratic mapping;
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