A Functional Inequality in Restricted Domains of Banach Modules

We investigate the stability problem for the following functional inequality parallel to alpha f((x + y)/2 alpha) + beta f((y + z)/2 beta) + gamma f((z + x)/2 gamma)parallel to <= parallel to f(x + y + z)parallel to on restricted domains of Banach modules over a C*-algebra. As an application we study the asymptotic behavior of a generalized additive mapping. Copyright (C) 2009 M. B. Moghimi et al.The third author was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2009-0070788). The authors would like to thank the referees for a number of valuable suggestions regarding a previous version of this paper