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Convex combination of analytic functions

Published:2017-03-29 Issue:1 Volume:15 Page:331-339
ISSN:2391-5455
Container-title:Open Mathematics
language:
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Author:

Cho Nak Eun¹,Jain Naveen Kumar²,Ravichandran V.²

Affiliation:

1. Department of Applied Mathematics, Pukyong National University, Busan 608-737, South Korea

2. Department of Mathematics, University of Delhi, Delhi-110007, Delhi, India

Abstract

Abstract Radii of convexity, starlikeness, lemniscate starlikeness and close-to-convexity are determined for the convex combination of the identity map and a normalized convex function F given by f(z) = α z+(1−α)F(z).

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2017-0021/pdf

Reference56 articles.

1. Radius problems for a class of analytic functions;Demonstratio Math,2006

2. Some radius results for univalent functions;J. Math. Anal. Appl,1995

3. On the largest disc mapped by sum of convex and starlike functions;Abstr. Appl. Anal.,2013

4. On starlike functions associated with parabolic regions;Ann. Univ. Mariae Curie-Skłodowska Sect. A,1991

5. Radii of starlikeness and convexity of functions defined by subordination with fixed second coefficients;Filomat,2012

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