Additive rho-functional inequalities in normed spaces

In this paper, we solve the additive rho-functional inequalities parallel to f(x + y) - f(x) - f(y) parallel to ??= parallel to rho(2f (x + y/2) - f(x) - f(y) parallel to (1) and parallel to 2f (x + y)/2) - f(x) - f(y) parallel to ??= parallel to rho(f (x + y) - f(x) - f(y)) parallel to, (2) where rho is a number with vertical bar rho vertical bar ?? 1. Using the fixed point method, we prove the Hyers-Ulam stability of the additive functional inequalities (1) and (2) in normed spaces. (C)2016 All rights reserved.J. Choi and J. Seong were supported by the Seoul Science High School R&E/I&D Program in 2014. C. Park was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2012R1A1A2004299)