# The Fifth and Sixth Coefficients for Bazilevič Functions $$\mathcal B_{1}(\alpha )$$ B 1 ( α )

The Fifth and Sixth Coefficients for Bazilevič Functions $$\mathcal B_{1}(\alpha )$$ B 1... Let f be analytic in $${\mathbb D}=\{z:|z|<1\}$$ D = { z : | z | < 1 } , with $$f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$$ f ( z ) = z + ∑ n = 2 ∞ a n z n and belong to the set of Bazilevič functions of logarithmic growth $${\mathcal B}_{1}(\alpha )$$ B 1 ( α ) defined for $$\alpha \ge 0$$ α ≥ 0 by $$\mathfrak {Re} \big \{ f'(z)\big (\frac{f(z)}{z}\big )^{\alpha -1}\big \}>0$$ Re { f ′ ( z ) ( f ( z ) z ) α - 1 } > 0 . Sharp bounds for $$|a_{5}|$$ | a 5 | , $$|a_{6}|$$ | a 6 | and the fifth coefficient of the inverse function are given when $$0\le \alpha \le 1$$ 0 ≤ α ≤ 1 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

# The Fifth and Sixth Coefficients for Bazilevič Functions $$\mathcal B_{1}(\alpha )$$ B 1 ( α )

, Volume 14 (4) – Jun 26, 2017
11 pages

/lp/springer_journal/the-fifth-and-sixth-coefficients-for-bazilevi-functions-mathcal-b-1-xSbb4zWCjH
Publisher
Springer International Publishing
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-017-0958-y
Publisher site
See Article on Publisher Site

### Abstract

Let f be analytic in $${\mathbb D}=\{z:|z|<1\}$$ D = { z : | z | < 1 } , with $$f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$$ f ( z ) = z + ∑ n = 2 ∞ a n z n and belong to the set of Bazilevič functions of logarithmic growth $${\mathcal B}_{1}(\alpha )$$ B 1 ( α ) defined for $$\alpha \ge 0$$ α ≥ 0 by $$\mathfrak {Re} \big \{ f'(z)\big (\frac{f(z)}{z}\big )^{\alpha -1}\big \}>0$$ Re { f ′ ( z ) ( f ( z ) z ) α - 1 } > 0 . Sharp bounds for $$|a_{5}|$$ | a 5 | , $$|a_{6}|$$ | a 6 | and the fifth coefficient of the inverse function are given when $$0\le \alpha \le 1$$ 0 ≤ α ≤ 1 .

### Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: Jun 26, 2017

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