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  Volume 9, Issue 1, Article 22
Some Properties of a New Class of Analytic Functions Defined in Terms of a Hadamard Product

    Authors: R.K. Raina, Deepak Bansal,  
    Keywords: Starlike function, Convex function, Close-to-convex function, Hadamard product, Ruscheweyh operator, Carlson and Schaffer operator, Subordination factor sequence, Schwarz function.  
    Date Received: 15/04/2007  
    Date Accepted: 12/01/2008  
    Subject Codes:

Primary 30C45.

    Editors: Hari M. Srivastava,  

In this paper we introduce a new class $ mathcal{H}(phi ,alpha ,beta )$ of analytic functions which is defined by means of a Hadamard product (or convolution) of two suitably normalized analytic functions. Several properties like, the 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.

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