Some properties of a new class of analytic functions defined in terms of a Hadamard product. (English) Zbl 1165.30339

Raina, R. K.; Bansal, Deepak

JIPAM, J. Inequal. Pure Appl. Math. 9, No. 1, Paper No. 22, 9 p. (2008).

Summary: In this paper we introduce a new class \( \mathcal{H}(\phi ,\alpha ,\beta )\) of analytic functions which is defined by means of the Hadamard product (or convolution) of two suitably normalized analytic functions. Several properties like coefficient bounds, growth and distortion theorems, radii of starlikeness, convexity and close-to-convexity are investigated. We further consider a subordination theorem, certain boundedness properties associated with partial sums, an integral transform of a certain class of functions, and some integral means inequalities. Several interesting consequences of our main results are also pointed out.

MSC:

30C45

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

starlike function; convex function; close-to-convex function; Hadamard product; Ruscheweyh operator; subordination factor sequence