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  Volume 7, Issue 3, Article 109
 
On Neighborhoods of Analytic Functions having Positive Real Part
    Authors: Shigeyoshi Owa, Nigar Yildirim, Muhammet Kamali,  
    Keywords: Function with positive real part, subordinate function, $delta -$neighborhood, convolution (Hadamard product).  
    Date Received: 10/11/05  
    Date Accepted: 15/07/06  
    Subject Codes:

Primary 30C45.

  
    Editors: Gabriela Kohr,  
 
    Abstract:

Two subclasses $ mathcal{P}left(frac{alpha -m}{n}right)$ and $ mathcal{P}^{prime }left(frac{alpha -m}{n}right)$ of certain analytic functions having positive real part in the open unit disk $ mathbb{U}$ are introduced. In the present paper, several properties of the subclass $ mathcal{P}left(frac{alpha -m}{n}right)$ of analytic functions with real part greater than $ frac{alpha -m}{n}$ are derived. For $ p(z)in mathcal{P}left(frac{alpha -m}{n}right)$ and $ delta geq 0,$ the $ delta -$neighborhood $ mathcal{N}_{delta }(p(z))$ of $ p(z)$ is defined. For $ mathcal{P}left(frac{alpha -m}{n}right)$, $ P^{prime }left(frac{alpha -m}{n}right)$, and $ N_{delta}(p(z))$, we prove that if $ p(z)in P^{prime }left(frac{alpha -m}{n}right)$, then $ N_{beta delta }(p(z))subset Pleft(frac{alpha -m}{n}right)$.

         
       
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