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

Authors:	E G Goluzina

Abstract:	Let M_k,λ(0≤λ≤1, k≥2) be the class of functions f(z)=1/z+a_o+a₁z+... that are regular and locally univalent for 0<⩛z⩛<1 and satisfy the condition $\mathop {\lim }\limits_{r \to 1 - } \int\limits_0^{2\pi } {\left\| {\operatorname{Re} J_\lambda \left( {re^{i\theta } } \right)} \right\|} d\theta \leqslant k\pi ,$ where J_λ(z)=λ(1+zf″(z)/f'(z))+(1-λ)zf'(z)/f(z). In the class M_k,λ we consider sorne coefficient problems and problems concerning distortion theorems. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 212, 1994, pp. 91–96. Translated by N. Yu. Netsvetaev.

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