7. Suppose f: D→C is holomorphic. Show that the diameter d= sup,, wED f(a)-f(w)of the image of f ...
7. Suppose f: D→C is holomorphic. Show that the diameter d= sup,, wED f(a)-f(w)of the image of f satisfies Moreover, it can be shown that equality holds precisely when f is linear, f(z)- Note. In connection with this result, see the relationship between the diameter of a curve and Fourier seri . es described in Problem 1, Chapter 4, Book I -, Layer d' whenever 0 < r < İ.] Hint 25,(0) =亦 ici r
7. Suppose f: D→C is holomorphic. Show that the diameter d= sup,, wED f(a)-f(w)of the image of f satisfies Moreover, it can be shown that equality holds precisely when f is linear, f(z)- Note. In connection with this result, see the relationship between the diameter of a curve and Fourier seri . es described in Problem 1, Chapter 4, Book I -, Layer d' whenever 0