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  Volume 8, Issue 2, Article 43
A New Subclass of $k$-Uniformly Convex Functions with Negative Coefficients

    Authors: Hari M. Srivastava, T.N. Shanmugam, C. Ramachandran, S. Sivasubramanian,  
    Keywords: Analytic functions; Univalent functions; Coefficient inequalities and coefficient estimates; Starlike functions; Convex functions; Close-to-convex functions; $k$-Uniformly convex functions; $k$-Uniformly starlike functions; Uniformly starlike functions; Hadamard product (or convolution); Extreme points; Radii of close-to-convexity, starlikeness and convexity; Integral operators.  
    Date Received: 31/05/07  
    Date Accepted: 15/06/07  
    Subject Codes:

Primary 30C45.

    Editors: Themistocles M. Rassias,  

The main object of this paper is to introduce and investigate a subclass $ mathcal{U}(lambda,alpha,beta,k)$ of normalized analytic functions in the open unit disk $ Delta$, which generalizes the familiar class of uniformly convex functions. The various properties and characteristics for functions belonging to the class $ mathcal{U}(lambda,alpha,beta,k)$ derived here include (for example) a characterization theorem, coefficient inequalities and coefficient estimates, a distortion theorem and a covering theorem, extreme points, and the radii of close-to-convexity, starlikeness and convexity. Relevant connections of the results, which are presented in this paper, with various known results are also considered.

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