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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hyers-Ulam-Rassias stability of Jensen’s equation and its application
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by Soon-Mo Jung PDF
Proc. Amer. Math. Soc. 126 (1998), 3137-3143 Request permission

Abstract:

The Hyers-Ulam-Rassias stability for the Jensen functional equation is investigated, and the result is applied to the study of an asymptotic behavior of the additive mappings; more precisely, the following asymptotic property shall be proved: Let $X$ and $Y$ be a real normed space and a real Banach space, respectively. A mapping $f: X \rightarrow Y$ satisfying $f(0)=0$ is additive if and only if $\left \| 2f\left [ (x+y)/2 \right ] - f(x) - f(y) \right \| \rightarrow 0$ as $\| x \| + \| y \| \rightarrow \infty$.
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Additional Information
  • Soon-Mo Jung
  • Affiliation: Mathematics Section, College of Science and Technology, Hong-Ik University, 339-800 Cochiwon, South Korea
  • Email: smjung@wow.hongik.ac.kr
  • Received by editor(s): March 19, 1997
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 3137-3143
  • MSC (1991): Primary 39B72
  • DOI: https://doi.org/10.1090/S0002-9939-98-04680-2
  • MathSciNet review: 1476142