TY - JOUR
AU - Park, Choonkil
PY - 2014
TI - Additive \(\rho\)--functional inequalities
JO - Journal of Nonlinear Sciences and Applications
SP - 296--310
VL - 7
IS - 5
AB - 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.
SN - ISSN 2008-1901
UR - http://dx.doi.org/10.22436/jnsa.007.05.02
DO - 10.22436/jnsa.007.05.02
ID - Park2014
ER -