Coefficients problems for families of holomorphic functions related to hyperbola
AbstractWe consider a family of analytic and normalized functions that are related to the domains ℍ(s), with a right branch of a hyperbolas H(s) as a boundary. The hyperbola H(s) is given by the relation $\begin{array}{} \frac{1}{\rho}=\left( 2\cos\frac{\varphi}{s}\right)^s\quad (0 \lt s\le 1,\, |\varphi| \lt (\pi s)/2). \end{array}$ We mainly study a coefficient problem of the families of functions for which zf′/f or 1 + zf″/f′ map the unit disk onto a subset of ℍ(s) . We find coefficients bounds, solve Fekete-Szegö problem and estimate the Hankel determinant.
2019 ◽
Vol 12
(02)
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pp. 1950017
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2019 ◽
Vol 38
(7)
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pp. 203-218
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2020 ◽
Vol 87
(3-4)
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pp. 165
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2000 ◽
Vol 62
(1)
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pp. 1-19
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