Exercise 5.  Let    be analytic in the disk    and suppose that    for  .  

5 (a).  Find a bound for  .  

Solution 5 (a).

See text and/or instructor's solution manual.

Solution.   Use  Theorem 6.16 (Maximum Modulus Principle) , and Theorem 6.17 (Cauchy's Inequalities):  

If    holds for all points ,  then  .

Here we have    ,  ,  and    so that  

                    ,  
               or
                    .  

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell