On preserving the univalence integral operator (Q2901297)
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scientific article; zbMATH DE number 6058314
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On preserving the univalence integral operator |
scientific article; zbMATH DE number 6058314 |
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19 July 2012
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derivative operator
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integral operator
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univalence
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0.9614434
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On preserving the univalence integral operator (English)
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This work deals with preserving the univalence of a certain integral operator defined by a generalized derivative operator defined on a family of normalized functions analytic in the unit disk. For this purpose, the authors introduce a new generalized derivative operator and define an integral operator. This operator reduces under special conditions of the defining parameters to an integral operator studied in [\textit{S. Bulut}, J. Inequal. Appl. 2008, Article ID 957042, 5 p. (2008; Zbl 1149.30015)]. A condition under which this integral operator is univalent is determined. Furthermore, it is shown that the univalence of this integral operator is preserved under certain sufficient conditions.
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