@Article{Park2014,
author="Choonkil Park",
title="Additive \(\rho\)--functional inequalities",
year="2014",
volume="7",
number="5",
pages="296--310",
abstract="In this paper, we solve the additive \(\rho\)-functional inequalities
\[\|f(x + y) - f(x) - f(y)\| \leq \| \rho( 2f (\frac{ x + y}{ 2}) - f(x) - f(y) ) \|, \qquad (1)\] ;
\[\|2f (\frac{ x + y}{ 2}) - f(x) - f(y)\| \leq \| \rho(f(x + y) - f(x) - f(y) ) \|, \qquad (2)\] ;
where \(\rho\) is a fixed non-Archimedean number with \(|\rho|<1\) or \(\rho\) is a fixed complex number with \(|\rho|<1\).
Using the direct method, we prove the Hyers-Ulam stability of the additive \(\rho\)-functional inequalities (1)
and (2) in non-Archimedean Banach spaces and in complex Banach spaces, and prove the Hyers-Ulam
stability of additive \(\rho\)-functional equations associated with the additive \(\rho\)-functional inequalities (1) and (2)
in non-Archimedean Banach spaces and in complex Banach spaces.",
issn="ISSN 2008-1901",
doi="10.22436/jnsa.007.05.02",
url="http://dx.doi.org/10.22436/jnsa.007.05.02"
}