Abstract
Let Mk,λ(0≤λ≤1, k≥2) be the class of functions f(z)=1/z+ao+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 Jλ(z)=λ(1+zf″(z)/f'(z))+(1-λ)zf'(z)/f(z). In the class Mk,λ we consider sorne coefficient problems and problems concerning distortion theorems.
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Literature Cited
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Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 212, 1994, pp. 91–96.
Translated by N. Yu. Netsvetaev.
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Goluzina, E.G. The value regions of initial coefficients in a certain class of meromorphic functions. J Math Sci 83, 745–749 (1997). https://doi.org/10.1007/BF02439201
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DOI: https://doi.org/10.1007/BF02439201