JIPAM

Some Generalized Convolution Properties Associated with Certain Subclasses of Analytic Functions  
 
  Authors: Shigeyoshi Owa, Hari M. Srivastava,  
  Keywords: Analytic functions, Hadamard product (or convolution), Generalized convolution, Cauchy-Schwarz inequality, Hölder inequality, Inclusion theorems.  
  Date Received: 05/03/02  
  Date Accepted: 06/04/02  
  Subject Codes:

30C45,26D15,30A10

  
  Editors: Gradimir V. Milovanovic,  
 
  Abstract:

For functions belonging to each of the subclasses $ mathcal{M}_{n}^{ast }left( alpha right) $ and $ mathcal{N}_{n}^{ast }left( alpha right) $ of normalized analytic functions in open unit disk $ mathbb{U},$ which are introduced and investigated in this paper, the authors derive several properties involving their generalized convolution by applying certain techniques based especially upon the Cauchy-Schwarz and Hölder inequalities. A number of interesting consequences of these generalized convolution properties are also considered.;


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