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We investigate the stability problem for the following functional inequality &#x2225;&#x03B1;f((x+y)/2&#x03B1;)+&#x03B2;f((y+z)/2&#x03B2;)+&#x03B3;f((z+x)/2&#x03B3;)&#x2225;&#x2264;&#x2225;f(x+y+z)&#x2225; on restricted domains of Banach modules over a C&#x2217;-algebra. As an application we study the asymptotic behavior of a generalized additive mapping

A Functional Inequality in Restricted Domains of Banach Modules