Properties of certain analytic functions associated with two boundary points
Abstract
For analytic functions f(z) in the closed unit disk U, two boundary points z1 and z2 such that α = (f'(z1)+f'(z2))/2 in f'(U) are considered. The object of the present paper is to discuss some interesting conditions for f(z) to be |f'(z)-1|<|1-α| in U with some examples.
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