A class of analytic functions based on convolution

A class of analytic functions based on convolution

We introduce a class <I>TS</I><SUB>p</SUB><SUP>g</SUP>(α) of analytic functions with negative coefficients defined by convolution with a fixed analytic function g(z)=z+<I>Σ</I><SUB>n=2</SUB><SUP>∞</SUP>b<SUB>n</SUB>z...

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Bibliographic Details
Main Authors: H. Silverman, K.G. Subramanian, R. Thirumalaisamy, T.V. Sudharsan
Format: Article
Language:English
Published: University Constantin Brancusi of Targu-Jiu 2010-09-01
Series:Surveys in Mathematics and its Applications
Subjects:
Analytic functions
Starlike functions
Convolution
Online Access:http://www.utgjiu.ro/math/sma/v05/p21.pdf
Description
Summary:We introduce a class <I>TS</I><SUB>p</SUB><SUP>g</SUP>(α) of analytic functions with negative coefficients defined by convolution with a fixed analytic function g(z)=z+<I>Σ</I><SUB>n=2</SUB><SUP>∞</SUP>b<SUB>n</SUB>z<SUP>n</SUP>, b<SUB>n</SUB>>0, |z|<1. We obtain the coefficient inequality, coefficient estimate, distortion theorem, a convolution result, extreme points and integral representation for functions in the class <I>TS</I><SUB>p</SUB><SUP>g</SUP>(α).
ISSN:1843-7265
1842-6298

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