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 -