Let f(z) be a holomorphic function in {∣z∣≤R} (0<R<∞). Define
M(r,f)=\max_{\vert z\vert=r} \vert f(z)\vert, A(r,f)=\max_{\vert z\vert=r} \text{Re}\{f(z)\}.
Show that
M(r,f) \le \frac{2r}{R-r}A(R,f)+\frac{R+r}{R-r} \vert f(0)\vert, \forall 0 \le r complex analysisinequalitiescollege contestsfunction