Abstract
For analytic functions f(z) in the closed unit disk \bar{U}, two boundary points z_1 and z_2 such that α= (f'(z_1)+f'(z_2))/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|<ρ|1-α| in U with some examples.
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