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A class of analytic functions defined by the Carlson-Shaffer operator
by Neng Xu   Dinggong Yang

Vol. 2 No. 1 (2007) P.91~P.102

ABSTRACT

The Carlson-Shaffer operator $L(a, c)f = \phi (a, c) \ast f$, where $f(z) = z +a_2z^2 + \dots$ is analytic in the unit disk $E =$ {$z: |z| < 1$} and $\phi(a, c; z)$ is an incomplete beta function, is used to define the class $T(a, c)$. An analytic function $f$ belongs to $T(a, c)$ if $L(a, c)f$ is starlike in $E$. The object of the present paper is to derive some properties of functions $f$ in the class $T(a, c)$.

KEYWORDS
Carlson-Shaffer operator, convex, convolution, starlike, sub-ordination

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 30C45

MILESTONES

Revised :
Accepted: