Neighbourhoods and Partial Sums of Starlike Functions Based on Ruscheweyh Derivatives

Volume 4, Issue 4, 2003

Article 64

SPATIAL BEHAVIOUR FOR THE HARMONIC VIBRATIONS IN PLATES OF KIRCHHOFF TYPE

¹THOMAS ROSY, ¹K.G. SUBRAMANIAN AND ²G. MURUGUSUNDARAMOORTHY

¹DEPARTMENT OF MATHEMATICS,
MADRAS CHRISTIAN COLLEGE,
TAMBARAM, CHENNAI , INDIA.

²DEPARTMENT OF MATHEMATICS,
VELLORE INSTITUTE OF TECHNOLOGY, DEEMED UNIVERSITY,
VELLORE, TN-632 014, INDIA.
E-Mail: gmsmoorthy@yahoo.com

Received 14 November, 2002; Accepted 26 March, 2003.
Communicated by: A. Lupas

ABSTRACT. In this paper a new class $S_{p}^{\lambda }\left( \alpha ,\beta \right)$ of starlike functions is introduced. A subclass $TS_{p}^{\lambda }\left( \alpha ,\beta \right)$ of $S_{p}^{\lambda }\left( \alpha ,\beta \right)$ with negative coefficients is also considered. These classes are based on Ruscheweyh derivatives. Certain neighbourhood results are obtained. Partial sums $f_{n}(z)$ of functions

in these classes are considered and sharp lower bounds for the ratios of real part of

to $f_{n}(z)$ and $% f^{\prime }(z)$ to $f_{n}^{\prime }(z)$ are determined.

Key words:
Univalent , Starlike , Convex.

2000 Mathematics Subject Classification:
30C45.

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