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http://dx.doi.org/10.11568/kjm.2014.22.2.317

AN ADDITIVE FUNCTIONAL INEQUALITY  

Lee, Sung Jin (Department of Mathematics Daejin University)
Park, Choonkil (Department of Mathematics Hanyang University)
Shin, Dong Yun (Department of Mathematics University of Seoul)
Publication Information
Korean Journal of Mathematics / v.22, no.2, 2014 , pp. 317-323 More about this Journal
Abstract
In this paper, we solve the additive functional inequality $${\parallel}f(x)+f(y)+f(z){\parallel}{\leq}{\parallel}{\rho}f(s(x+y+z)){\parallel}$$, where s is a nonzero real number and ${\rho}$ is a real number with ${\mid}{\rho}{\mid}$ < 3. Moreover, we prove the Hyers-Ulam stability of the above additive functional inequality in Banach spaces.
Keywords
Jordan-von Neumann functional equation; Hyers-Ulam stability; functional inequality;
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