consider the following theorem,and prove if uniqueness be preserved if f'(z)>0 is replaced by f'(z)<0 Theorem 1. Given any simply connected region N which is not the whole plane, and a point zo e N, there exists a unique analytic function f(z) in 2, normalized by the conditions f(z0) = 0, f'(zo) > 0, such that f(2) defines a one-to-one mapping of 2 onto the disk |w| < 1.
consider the following theorem,and prove if uniqueness be preserved if f'(z)>0 is replaced by f'(z)<0 Theorem 1. Given any simply connected region N which is not the whole plane, and a point zo e N, there exists a unique analytic function f(z) in 2, normalized by the conditions f(z0) = 0, f'(zo) > 0, such that f(2) defines a one-to-one mapping of 2 onto the disk |w| < 1.
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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Transcribed Image Text:consider the following theorem,and prove if uniqueness be preserved if f'(z)>0 is replaced by f'(z)<0
Theorem 1. Given any simply connected region N which is not the whole
plane, and a point zo e 1, there exists a unique analytic funclion f(z) in 2,
normalized by the conditions f(zo) = 0, f'(2o) > 0, such that f(2) defines a
one-to-one mapping of 2 onto the disk w < 1.
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