IJPAM: Volume 78, No. 1 (2012)

A SUBCLASS OF ANALYTIC FUNCTIONS
WITH NEGATIVE COEFFICIENTS

Li Xiao-Fei$^1$, Wang An-Ping$^2$
$^{1,2}$College of Technology and Engineering
Yangtze University
Jingzhou, 434020, P.R. CHINA


Abstract. In this paper, we introduce a class of functions $T_{n}^{p} (\alpha ,\beta )$ which are analytic in the unit disk. We obtain a necessary and sufficient condition for a function to be in $T_{n}^{p} (\alpha ,\beta )$, and radii of close-to convexity, starlikeness and convexity. Further, an application in the fractional calculus for functions in $T_{n}^{p} (\alpha ,\beta )$ is given.

Received: March 15, 2012

AMS Subject Classification: 30C45

Key Words and Phrases: negative coefficients, close-to convexity, starlikeness, convexity, fractional calculus

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 1