On a class of regular functions. (Russian) Zbl 0696.30014
Actual questions of function theory, Rostov, 143-147 (1987).
Summary: [For the entire collection see Zbl 0697.00014.]
Exact estimations are derived for the coefficients of the values \(| f(z)|\) and \(| f'(z)|\). \(\lambda\)-spiral shapedness is investigated for the class \(S^{\lambda}_ n(A,B)\) of functions \[ f(z)=z+a_{n+1}z^{n+1}+a_{n+2}z^{n+2}+... \] that are regular in the circle \(| z| <1\) and satisfy the condition \[ e^{i\lambda}(zf'(z))/(f(z))\quad \prec \quad [(1+Az)/(1-Bz)]\cos \lambda +i \sin \lambda, \] where \(\prec\) denotes the subordination operator, A and B are complex numbers, \(| B| \leq 1\), \(| A| \leq 1\), \(A\neq -B\) and \((-\pi)/2<\lambda <(\pi /2)\).
Exact estimations are derived for the coefficients of the values \(| f(z)|\) and \(| f'(z)|\). \(\lambda\)-spiral shapedness is investigated for the class \(S^{\lambda}_ n(A,B)\) of functions \[ f(z)=z+a_{n+1}z^{n+1}+a_{n+2}z^{n+2}+... \] that are regular in the circle \(| z| <1\) and satisfy the condition \[ e^{i\lambda}(zf'(z))/(f(z))\quad \prec \quad [(1+Az)/(1-Bz)]\cos \lambda +i \sin \lambda, \] where \(\prec\) denotes the subordination operator, A and B are complex numbers, \(| B| \leq 1\), \(| A| \leq 1\), \(A\neq -B\) and \((-\pi)/2<\lambda <(\pi /2)\).
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C80 | Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination |
