Korean J. Math. Vol. 22 No. 2 (2014) pp.317-323
DOI: https://doi.org/10.11568/kjm.2014.22.2.317

An additive functional inequality

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Published: Jun 26, 2014
Keywords:
Jordan-von Neumann functional equation, Hyers-Ulam stability, functional inequality.
Mathematics Subject Classification:
39B62, 39B72

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Sung Jin Lee
Department of Mathematics Daejin University Kyeonggi 487-711, Korea
Choonkil Park
Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea
Dong Yun Shin
Department of Mathematics University of Seoul Seoul 130-743, Korea

Abstract

In this paper, we solve the additive functional inequality
$$
\|f(x)+f(y)+f(z)\| \le \left\| \rho f\left( s (x+y+z)\right)\right\| , $$
where $s$ is a nonzero real number and $\rho$ is a real number with $|\rho| < 3$.

Moreover, we prove the Hyers-Ulam stability of the above additive functional inequality in Banach spaces.



Article Details

Supporting Agencies

This work was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education Science and Technology (NRF-2012R1A1A2004299) and (NRF-2010-0021792).

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