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A unified class of analytic functions with negative coefficients

  • G. MurugusundaramoorthyEmail author
  • T. Rosy
  • K. Muthunagai
Article

Abstract

Making use of the convolution product, we introduce a unified class of analytic functions with negative coefficients. Also, we obtain the coefficient bounds, extreme points, and radius of starlikeness for functions belonging to the generalized class P g T (λ, α, β). Furthermore, partial sums f k (z) of functions f(z) in the class P g (λ, α, β) are considered and sharp lower bounds for the ratios of the real parts of f(z) to f k (z) and f′(z) to f′ k (z) are determined. Relevant connections of the results with various known results are also considered.

Key words and phrases

Analytic univalent starlikeness convexity Hadamard product (convolution) Convolution product uniformly convex uniformly starlike functions 

2000 Mathematics Subject Classification

30C45 

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  • G. Murugusundaramoorthy
    • 1
    Email author
  • T. Rosy
    • 2
  • K. Muthunagai
    • 3
  1. 1.School of Science and HumanitiesVIT UniversityVelloreIndia
  2. 2.Department of MathematicsMadras Christian CollegeChennaiIndia
  3. 3.Department of MathematicsRajalakshmi Engineering CollegeChennaiIndia

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