Approximate additive and quadratic mappings in 2-Banach spaces and related topics

Cho, Y. J.; Park, C.; Eshaghi Gordji, M.

doi:10.22075/ijnaa.2012.55

Approximate additive and quadratic mappings in 2-Banach spaces and related topics

Document Type : Research Paper

Authors

Y. J. Cho ¹

C. Park ²

M. Eshaghi Gordji ³

¹ Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea

² Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea

³ Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran.

10.22075/ijnaa.2012.55

Abstract

Won-Gil Park [Won-Gil Park, J. Math. Anal. Appl., 376 (1) (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. One can easily see that all results of this paper are incorrect. Hence the control functions in all theorems of this paper are not correct. In this paper, we correct these results.

Keywords

Hyers-Ulam Stability

Cauchy Functional Equation

Jensen Functional Equation

quadratic functional equation