(3) 5. Suppose that f : D[0, 1] → D[0, 1] is holomorphic, prove that f'(2)...
[3] 5. Suppose that f: D[0,1] for all z E D[0, 1] D[0,1] is holomorphic, prove that \f'(z) < 1/(1 - 121)2
[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]
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]
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
[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)?
[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].
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).)
(5) Let qe Q. Suppose that a <b, 0<c<d, and that f : [a, b] → [c, d]. If f is integrable on [a,b], then prove that * (t)dt) = f'(x) for all 3 € (a, b).
.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
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?