Abstract
The goal of this manuscript to establish the best possible estimate on coefficient functionals like Hermitian-Toeplitz determinant of secoend order involving logarithmic coefficients, initial logarithmic inverse coefficients and initial order Schwarzian derivatives of the Ozaki close-to-convex functions.
Results & Lemmas (5)
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Theorem 2.2 · coeff
Theorem 2.2. Let the function be in the class. Then <span id="page-5-0"></span> All inequalities are sharp for the function given in (1.1).
Theorem 2.2. Let the function $f(z) = z + \sum_{n=2}^{\infty} a_n z^n$ be in the class $\mathcal{F}$ . Then
<span id="page-5-0"></span>
$$|\Gamma_1| \le \frac{3}{4}, \quad |\Gamma_2| \le \frac{11}{16}, \quad |\Gamma_3| \le \frac{7}{8}.$$
All inequalities are sharp for the function $f_1$ given in (1.1).
Theorem 2.3 · coeff
Theorem 2.3. Let the function be in the class. Then The inequality is sharp for the function given by (1.2).
Theorem 2.3. Let the function $f(z) = z + \sum_{n=2}^{\infty} a_n z^n$ be in the class $\mathcal{F}$ . Then
The inequality is sharp for the function $f_2$ given by (1.2).
Theorem 2.4 · coeff
Theorem 2.4. Let the function be in the class. Then (a), (b). Both the inequalities are sharp for the function given by (1.1).
Theorem 2.4. Let the function $f(z) = z + \sum_{n=2}^{\infty} a_n z^n$ be in the class $\mathcal{F}$ . Then
(a)
$$|A_3 - A_2| \le 4$$
,
(b)
$$|\Gamma_3 - \Gamma_2| \le \frac{25}{16}$$
.
Both the inequalities are sharp for the function given by (1.1).
Theorem 3.1 · coeff
Theorem 3.1. Let be in the class. Then The upper and lower bound are sharp for the function and given by (1.3) and (1.4) respectively.
Theorem 3.1. Let $f(z) = z + \sum_{n=2}^{\infty} a_n z^n$ be in the class $\mathcal{G}$ . Then
$$-\frac{1}{144} \le T_{2,1}(F_f/\gamma) \le \frac{15}{256}.$$
The upper and lower bound are sharp for the function $g_1$ and $g_2$ given by (1.3) and (1.4) respectively.
Theorem 3.3 · coeff
Theorem 3.3. Let the function be in the class. Then and. The both the inequalities are sharp for the function given by (1.3).
Theorem 3.3. Let the function $f(z) = z + \sum_{n=2}^{\infty} a_n z^n$ be in the class $\mathcal{G}$ . Then
$$|S_3| \le \frac{3}{2}$$
and $|S_4| \le 6$ .
The both the inequalities are sharp for the function given by (1.3).
Function classes studied:
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