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7. Let f be analytic in D = {|z| ≤ 1}. Assume that |f(z)| ≤ 1 for |z| = 1. Show that (a) [f" (0)| ≤ 2, (b) f(") ()| ≤8

7. Let f be analytic in D = {|z| ≤ 1}. Assume that |f(z)| ≤ 1 for |z| = 1. Show that (a) [f" (0)| ≤ 2, (b) f(") ()| ≤8

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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part a and b. thank you

7. Let f be analytic in D = {|z| ≤ 1}. Assume that |ƒ(z)| ≤ 1 for |z| = 1. Show that (a) |ƒ" (0)| ≤ 2, (b) |ƒ(") (½)| ≤ 8
Transcribed Image Text:7. Let f be analytic in D = {|z| ≤ 1}. Assume that |ƒ(z)| ≤ 1 for |z| = 1. Show that (a) |ƒ" (0)| ≤ 2, (b) |ƒ(") (½)| ≤ 8
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