IJPAM: Volume 53, No. 3 (2009)

COEFFICIENT INEQUALITIES FOR CERTAIN CLASSES
RELATED TO SALAGEAN OPERATOR AND APPLICATIONS

Toshio Hayami$^1$, Shigeyoshi Owa$^2$
$^{1,2}$Department of Mathematics
Kinki University
Higashi-Osaka, Osaka, 577-8502, JAPAN
$^1$e-mail: ha_ya_to112@hotmail.com
$^2$e-mail: owa@math.kindai.ac.jp


Abstract.For functions $f(z)$ which are analytic in the open unit disk $\mathbb{U}$, generalization operator $D^j f(z)$ of ${\rm S\check{a}l\check{a}gean}$ operator is introduced. With the operator $D^j f(z)$, the subclass $\mathcal{S}_j^m(\alpha)$ is defined. Some interesting sufficient conditions involving coefficient inequalities for $f(z)$ to be in the class $\mathcal{S}_j^m(\alpha)$ are discussed. Also, consequences of coefficient inequalities for differential subordination are considered.

Received: April 27, 2009

AMS Subject Classification: 30C45

Key Words and Phrases: coefficient inequality, analytic function, univalent function, strongly starlike function, ${\rm S\check{a}l\check{a}gean}$ operator, differential subordination

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 3