Geodesic
On the Univalence of an Integral on Subclasses of Meromorphic Functions
Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 92-99

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We study the integral operator $P_\lambda[f](\zeta)=\int_{\zeta_0}^\zeta\bigl(f'(t)\bigr)^\lambda dt$, $|\zeta|>1$, 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. 
@article{MZM_2001_69_1_a7,
     author = {I. R. Nezhmetdinov},
     title = {On the {Univalence} of an {Integral} on {Subclasses} of {Meromorphic} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {92--99},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a7/}
}
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I. R. Nezhmetdinov. On the Univalence of an Integral on Subclasses of Meromorphic Functions. Matematičeskie zametki, Tome 69 (2001) no. 1, pp. 92-99. http://geodesic.mathdoc.fr/item/MZM_2001_69_1_a7/