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Coefficient Estimates in a Class of Strongly Starlike Functions

Janusz Sokół · 2009 📄 find paper →

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Abstract

In this paper we consider some coefficient estimates in the subclass SL∗of strongly starlike functions defined by a certain geometric condition.

Results & Lemmas (3)

Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.

Theorem 1. Theorem 1. If the function f(z) = z + a2z2 + a3z3 + · · · belongs to the class SL∗, then (4) ∞ X k=2 (k2 −2)|ak|2 ≤1.
Theorem 1. If the function f(z) = z + a2z2 + a3z3 + · · · belongs to the class SL∗, then (4) ∞ X k=2 (k2 −2)|ak|2 ≤1.
Corollary 1. Corollary 1. If the function f(z) = z +a2z2 + a3z3 + · · · belongs to the class SL∗, then |ak| ≤ r 1 k2 −2 for k ≥2.
Corollary 1. If the function f(z) = z +a2z2 + a3z3 + · · · belongs to the class SL∗, then |ak| ≤ r 1 k2 −2 for k ≥2.
Theorem 2. Theorem 2. If the function f(z) = P∞ k=1 akzk belongs to the class SL∗, then (5) |a2| ≤1/2, |a3| ≤1/4, |a4| ≤1/6. Those estimations are…
Theorem 2. If the function f(z) = P∞ k=1 akzk belongs to the class SL∗, then (5) |a2| ≤1/2, |a3| ≤1/4, |a4| ≤1/6. Those estimations are sharp.

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