HW5 - f z = a has a solution in D(i.e the equation f z = a...

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MATH 6322, Complex Analysis Fall 2011, HW#5 Due date: Wed., Oct 5, 2011 Chapter 5: 5, 7, 8, 10acf, 11, 16 Extra Problems : Extra 1 : Let { f n } be a sequence of holomorphic functions on an open set D , and assume that it converges to a non-constant function f uniformly on every compact subsets of D . Prove that if the equation
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Unformatted text preview: f ( z ) = a has a solution in D (i.e. the equation f ( z ) = a is solvable on D ), where a is some complex number, then for n big enough, the equation f n ( z ) = a is also solvable on D (i.e the equation f n ( z ) = a has at least one solution in D ). 1...
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