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Partial sums of certain analytic and univalent functions. (English) Zbl 1092.30019
Summary: We study the ratio of a function of the form $f(z) = z + \sum^\infty_{k=2} a_k z^k$ to its sequence of partial sums of the form $$f_n(z) = z + \sum^n_{k=2} a_k z^k$$. Also, we will determine sharp lower bounds for $$\text{Re} \{f(z)/f_n(z)\}$$, $$\text{Re} \{f_n(z)/f(z)\}$$, $$\text{Re}\{f^\prime(z)/f^\prime_n(z)\}$$ and $$\text{Re}\{f^\prime_n(z)/f^\prime (z)\}$$.

##### MSC:
 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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