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Coefficient inequalities for a subclass of Bazilevič functions

机译：Coefficient inequalities for a subclass of Bazilevič functions

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摘要

Let f be analytic in D={z:|z|  1}{mathbb{D}}={z:|zmathrm{|hspace{0.17em}lt hspace{0.17em}1}} with f(z)=z+∑n=2∞anznf(z)=z+{sum }_{nmathrm{=2}}^{infty }{a}_{n}{z}^{n}, and for α ≥ 0 and 0 λ ≤ 1, let ℬ1(α,λ){ {mathcal B} }_{1}(alpha ,lambda ) denote the subclass of Bazilevič functions satisfying |f′(z)(zf(z))1−α−1|λleft|f^{prime} (z){left(frac{z}{f(z)}right)}^{1-alpha }-1right|lt lambda for 0 λ ≤ 1. We give sharp bounds for various coefficient problems when f∈ℬ1(α,λ)fin { {mathcal B} }_{1}(alpha ,lambda ), thus extending recent work in the case λ = 1.

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