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 Mat. Zametki, 2001, Volume 69, Issue 1, Pages 92–99 (Mi mz486)

On the Univalence of an Integral on Subclasses of Meromorphic Functions

I. R. Nezhmetdinov

Kazan State University

Abstract: We study the integral operator $P_\lambda[f](\zeta)=\int_{\zeta_0}^\zeta(f'(t))^\lambda dt$, $|\zeta|>1$, acting on the class $\Sigma$ of functions meromorphic and univalent in the exterior of the unit disk. We refine the ranges of the parameter $\lambda$ for which the operator preserves univalence either on $\Sigma$ or on its subclasses consisting of convex functions. As a consequence, a two-sided estimate is deduced for the separating constant in the sufficient condition for the univalent solvability of exterior inverse boundary-value problems.

DOI: https://doi.org/10.4213/mzm486

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English version:
Mathematical Notes, 2001, 69:1, 81–87

Bibliographic databases:

UDC: 517.546

Citation: I. R. Nezhmetdinov, “On the Univalence of an Integral on Subclasses of Meromorphic Functions”, Mat. Zametki, 69:1 (2001), 92–99; Math. Notes, 69:1 (2001), 81–87

Citation in format AMSBIB
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