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  Volume 3, Issue 3, Article 42
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:


    Editors: Gradimir V. Milovanovic,  

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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