A GENERALIZED ADDITIVE FUNCTIONAL INEQUALITY IN BANACH SPACES

In this paper, we investigate the Hyers-Ulam stability of the following function inequalityparallel to af(x) + bf(y) + cf(z)parallel to <= parallel to f(alpha x + beta y + gamma z)parallel to (1 <vertical bar a + b + c vertical bar)in Banach spaces.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), G. Lu was supported by supported by Doctoral Science Foundation of Liaoning Province, China, by Hall of Liaoning Province Science and Technology (No. 20121055), and D. Y. Shin was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2010-0021792)