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    STUDIA MATHEMATICA - Issue no. 4 / 2021  
         
  Article:   HARMONIC MAPPINGS AND ITS DIRECTIONAL CONVEXITY.

Authors:  POONAM SHARMA, OMENDRA MISHRA.
 
       
         
  Abstract:  
DOI: 10.24193/subbmath. 2021.4.07

Published Online: 2021-12-14
Published Print: 2021-12-30
pp. 677-690

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For any $mu _{j} (mu _{j}in mathbb{C},leftvert mu _{j} ightvert =1,j=1,2)$, we consider the rotations $f_{mu _{1}}$ and $F_{mu _{2}}$ of right half-plane harmonic mappings $f,Fin S_{mathcal{H}}$ which are CHD with the prescribed dilatations $omega _{f}(z)=left( a-z ight) /left( 1-az ight) $ for some $a$ $left( -1
Keywords: Harmonic functions, half-plane mappings, convexity in one direction, harmonic convolution, directional convexity, Rouche''s theorem.

Mathematics Subject Classification (2010): 31A05, 30C45, 30C55.
 
         
     
         
         
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