Can you solve this problem using a triangular keyhole contour as the method? This exercise comes from Stein & Shakarchi, ch 2 # 6.Let be an open subset of C, and let T C be a triangle whose interior is also containedin . Suppose that f is a function holomorphic in except possibly at a point w inside T.Prove that if f is bounded in an open neighborhood of w, thenf₁ f(z)dz = 0

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function holomorphic in 2 except p in an open neighborhood of w, the

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 10E: For each of the following parts, give an example of a mapping from E to E that satisfies the given...

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Question

Can you solve this problem using a triangular keyhole contour as the method?

This exercise comes from Stein & Shakarchi, ch 2 # 6.
Let be an open subset of C, and let T C be a triangle whose interior is also contained
in . Suppose that f is a function holomorphic in except possibly at a point w inside T.
Prove that if f is bounded in an open neighborhood of w, then
f₁ f(z)dz = 0

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