Ma-Minda φ-classes studied in this paper:
Abstract
Bounds established for second Hankel and Toeplitz determinants with entries determined by logarithmic coefficients of starlike functions mapping the unit disk onto a petal-shaped domain.
Results & Lemmas (2)
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 3.2
Theorem 3.2. Let, then <span id="page-6-4"></span> The above inequality is sharp.
Theorem 3.2. Let $f \in \mathcal{S}_{\rho}^*$ , then
<span id="page-6-4"></span>
$$\frac{1}{16} \le |H_{2,1}(F_{f^{-1}}/2)| \le \frac{1}{9}.\tag{3.12}$$
The above inequality is sharp.
Theorem 4.2
Theorem 4.2. Let, then The above inequality is sharp.
Theorem 4.2. Let $f \in \mathcal{S}_{\rho}^*$ , then
$$\frac{1}{16} \le |T_{2,1}(F_{f^{-1}}/2)| \le \frac{5}{4}.$$
The above inequality is sharp.
Function classes studied:
Coefficient bounds & claims (9)
Machine-extracted from the paper text - useful for cross-referencing, not a verified fact.
coefficient_bound
H_{2,1}(F_f/2) ≤ 1/16 for class S*_rho (sharp) [Theorem 3.1]
coefficient_bound
H_{2,1}(F_f/2) (lower) ≤ 1/72 for class S*_rho (sharp) [Theorem 3.1]
coefficient_bound
H_{2,1}(F_{f^{-1}}/2) ≤ 1/9 for class S*_rho (sharp) [Theorem 3.2]
coefficient_bound
H_{2,1}(F_{f^{-1}}/2) (lower) ≤ 1/16 for class S*_rho (sharp) [Theorem 3.2]
coefficient_bound
T_{2,1}(F_f/2) ≤ 1/2 for class S*_rho (sharp) [Theorem 4.1]
coefficient_bound
T_{2,1}(F_f/2) (lower) ≤ 1/16 for class S*_rho (sharp) [Theorem 4.1]
coefficient_bound
T_{2,1}(F_{f^{-1}}/2) ≤ 5/4 for class S*_rho (sharp) [Theorem 4.2]
coefficient_bound
T_{2,1}(F_{f^{-1}}/2) (lower) ≤ 1/16 for class S*_rho (sharp) [Theorem 4.2]
function_family
Class S*_rho: f in A with zf'/f subordinate to 1+arcsinh(z), mapping D onto petal-shaped domain
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