The value regions of initial coefficients in a~certain class of meromorphic functions

E. G. Goluzina

Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 12, Tome 212 (1994), pp. 91-96

Résumé

Let $M_{k,\lambda}$ ($0\le\lambda\le1$, $k\ge2$) be the class of functions $$ f(z)=1/z+a_0+a_1z+\dots, $$ that are regular and locally univalent for $0|z|1$ and satisfy the condition $$ \lim_{r\to1-}\int_0^{2\pi}|\operatorname{Re}J+\lambda(re^{i\theta})|\,d\theta\le k\pi, $$ where $$ J_\lambda(z)=\lambda(1+zf''(z)/f'(z))+(1-\lambda)zf'(z)/f(z). $$ In the class $M_{k,\lambda}$ we consider sorne coefficient problems and problems concerning distortion theorems. Bibliography: 6 titles.