Abstract
In this paper, we introduce an additive functional inequality and a quadratic functional inequality in normed spaces, and prove the Hyers-Ulam stability of the functional inequalities in Banach spaces. Furthermore, we introduce an additive functional inequality and a quadratic functional inequality in non-Archimedean normed spaces, and prove the Hyers-Ulam stability of the functional inequalities in non-Archimedean Banach spaces.
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Supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (Grant No. NRF-2012R1A1A2004299)
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Park, C. Functional inequalities in non-Archimedean normed spaces. Acta. Math. Sin.-English Ser. 31, 353–366 (2015). https://doi.org/10.1007/s10114-015-4278-5
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DOI: https://doi.org/10.1007/s10114-015-4278-5
Keywords
- Jordan-von Neumann functional equation
- non-Archimedean normed space
- Banach space
- Hyers-Ulam stability
- functional inequality