[3] 5. Suppose that f: D[0,1] for all z E D[0, 1] D[0,1] is holomorphic, prove...
(3) 5. Suppose that f : D[0, 1] → D[0, 1] is holomorphic, prove that f'(2) < 1/(1 - 121) for all z e D[0,1].
[3] 5. Suppose that f: D[0, 1] → D[0, 1] is holomorphic, prove that \f'(x) < 1/(1 - 1z| for all z e D[0, 1]. [3] 5. Suppose that f: D[0, 1] → D[0, 1] is holomorphic, prove that f'(x) < 1/(1-1-12 for all z e D[0, 1]
Please don't use schwarz pick lemma 5.17. Suppose f : D[0,1] → D[0,1] is holomorphic. Prove that for z1 <1, 1 |f'(2) 1 - 12
help with thus problem but not using schwoz-pick lemma [3] 5. Suppose that f: D[0,1] → D[0,1] is holomorphic, prove that f'(x) < 1/(1 - 1-1) for all z € D[0, 1]
[3] 5. Suppose that f: D[0,1] for all z E D(0,1) D[0,1] is holomorphic, prove that f'() 5 1/(1 - 121)?
Exercise 3 Let f be an analytic function on D(0,1). Suppose that f(z) < 1 for all z € C and f() = 0. Show that G) . (Hint: use the function g(z) = f(2).)
u(20) for all z e D. Prove tha E C:0<zl<2) and Cr be the positively oriented 9 (10) Suppose that f is analytic in the deleted disk B2(0) C be the positi that If(2)l S M<oo for all z e B2(0). If 0 TS circle |zl r. Show that S 1, then let Cr r | 1= f(z) dz = 0. (Hint: why is the value of (1) the same if C, is replaced by C?
[3] 5. Suppose that f: D[0, 1] → D[0, 1] is holomorphic, prove that [f'(x) = 1/(1 – )2 for all z e D[0, 1].
Sketch the graph that possesses the characteristics listed below. f'(3) = 0,1" (3) <0, f(3) = 5; f'(-1)= 0, f'(-1)>0, f(-1)= -1;f" (1) = 0, f(1) = 2 Choose the correct graph below. OA. OB O C. OD. 10
.Suppose that f : D[0, 1] → D[0, 1] is holomorphic, prove that |f 0 (z)| ≤ 1/(1 − |z|) ^2 for all z ∈ D[0, 1]. is there any way not to use the Schwartz' lemma