A CLASS OF MULTIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS DEFINED BY CONVOLUTION

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 43, Issue 1, 2006, pp.179-188
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2006.43.1.179

Title & Authors

A CLASS OF MULTIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS DEFINED BY CONVOLUTION

Ali Rosihan M.; Khan M. Hussain; Ravichandran V.; Subramanian K.G.;

Ali Rosihan M.; Khan M. Hussain; Ravichandran V.; Subramanian K.G.;

Abstract

For a given p-valent analytic function g with positive coefficients in the open unit disk , we study a class of functions satisfying $$\frac 1 {p}{\Re}\;(\frac {z(f*g)'(z)} {(f*g)(z)})\;>\;\alpha\;(0{\leq}\;\alpha\;<\;1;z{\in}{\Delta})$$ Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special cases.

Keywords

starlike function;convolution;subordination;negative coefficients;

Language

English

Cited by

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