TY - JOUR AU - Park, Yuanfeng AU - Lu, Yinhua AU - Cui, Gang AU - Jin, Choonkil PY - 2017 TI - Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces JO - Journal of Nonlinear Sciences and Applications SP - 104--110 VL - 10 IS - 1 AB - In this paper, we solve the quadratic \(\rho\)-functional inequalities \[\|f(x+y)+f(x-y)-2f(x)-2f(y)\|\leq\|\rho(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y))\|,\] where \(\rho\) is a fixed complex number with \(|\rho|<1\), and\[\|4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)\|\leq\|\rho(f(x+y)+f(x-y)-2f(x)-2f(y))\|,\] where \(\rho\) is a fixed complex number with \(|\rho|<1\). Using the direct method, we prove the Hyers-Ulam stability of the quadratic \(\rho\)-functional inequalities (1) and (2) in \(\beta\)- homogeneous complex Banach spaces. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.01.10 DO - 10.22436/jnsa.010.01.10 ID - Park2017 ER -