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    STUDIA MATHEMATICA - Issue no. 3 / 2010  
         
  Article:   DUALITY FOR HADAMARD PRODUCTS APPLIED TO CERTAIN CONDITION FOR α-STARLIKENESS.

Authors:  .
 
       
         
  Abstract:  Let P(α, β), α > 0, β < 1, denote the class of all analytic functions f in the unit disc with the normalization f(0) = 1, f’ (0) = 1 and satisfying the condition  for some φ Є R. In this paper we find conditions on α, β so that P(α, β) S*(μ), where μ < 1 is given and S*(μ) denote the class of starlike function of order μ. We take advantage of the Ruscheweh’s Duality theory.

Key words and phrases. Duality principle, dual set, Hadamard product, Starlike functions, convex functions, functions with positive real part, Gaussian hypergeometric function
 
         
     
         
         
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