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  Volume 6, Issue 1, Article 22
 
A Class of Multivalent Functions with Positive Coefficients Defined by Convolution
    Authors: Rosihan M. Ali, M. Hussain Khan, V. Ravichandran, K.G. Subramanian,  
    Keywords: Starlike function, Ruscheweyh derivative, Convolution, Positive coefficients, Coefficient inequalities, Growth and distortion theorems.  
    Date Received: 12/12/04  
    Date Accepted: 27/01/05  
    Subject Codes:

30C45

  
    Editors: Herb Silverman,  
 
    Abstract:

For a given $ p$-valent analytic function $ g$ with positive coefficients in the open unit disk $ Delta$, we study a class of functions $ f(z)=z^p+sum_{n=m}^infty a_nz^n$, $ a_ngeq 0$ satisfying

$displaystyle frac{1}{p}Releft( frac{z(f*g)^{prime}(z)}{(f*g)(z)}right) alpha quad left( zinDelta; 1alphafrac{m+p}{2p} right). $
Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special cases.

         
       
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