Author’s abstract: Let U(p) denote the family of functions f(z) meromorphic and univalent in \(| z| <1\), having a simple pole at p, \(0<p<1\), and normalized by \(f(0)=0\), \(f'(0)=1\). Let S(p) denote the family of functions f(z) regular and univalent in the open unit disk slit along the segment \(p\leq z<1\) and normalized by \(f(0)=0\), \(f'(0)=1\). The author obtains the minimum of \(| f(z)|\), \(| z| =r\), \(0<r<1\), the maximum of \(| f(z)|\), \(| z| =r\), \(0<r<p\) and the maximum of \(| f'(z)|\), \(| z| =r\), \(0<r<p\), for \(f\in S(p)\). He also obtains the maximum of \(| f(z)|\), \(| z| =r\), \(p<r<1\) for \(f\in U(p)\). In all cases the bound is uniquely assumed for the function \(z[1-(p+p^{-1})z+z^ 2]^{-1}\). In addition the author obtains the exact set of values which can be omitted by some function in U(p).