Geodesic
On an estimate of a functional in the class of holomorphic univalent functions
Mathematica Bohemica, Tome 118 (1993) no. 3, pp. 281-296

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Let $S$ denote the class of functions $f(x)=z+a_2z^2+a_3z^3+\ldots$ univalent and holomorphic in the unit disc $\Delta = \{z:\left|z\right|1\}$. In the paper we obtain an estimate of the functional $\left|a_3-ca^2_2\right|+c\left|a_2\right|^n$ in the class $S$ for arbitrarily fixed $x\in \bold R$ and $n=1,2,3,\ldots$. Hence, for some special values of the parameters, we obtain estimates of several interesting functionals and numerous applications. A few open problems of a similar type are also formulated.
Let $S$ denote the class of functions $f(x)=z+a_2z^2+a_3z^3+\ldots$ univalent and holomorphic in the unit disc $\Delta = \{z:\left|z\right|1\}$. In the paper we obtain an estimate of the functional $\left|a_3-ca^2_2\right|+c\left|a_2\right|^n$ in the class $S$ for arbitrarily fixed $x\in \bold R$ and $n=1,2,3,\ldots$. Hence, for some special values of the parameters, we obtain estimates of several interesting functionals and numerous applications. A few open problems of a similar type are also formulated.
DOI : 10.21136/MB.1993.125927
Classification : 30C50
Keywords: estimation of functionals; Koebe function; univalent function; coefficient problem 
Jakubowski, Zbigniew Jerzy; Zyskowska, Krystyna. On an estimate of a functional in the class of holomorphic univalent functions. Mathematica Bohemica, Tome 118 (1993) no. 3, pp. 281-296. doi: 10.21136/MB.1993.125927
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