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On harmonic univalent functions defined by a generalized Ruscheweyh derivatives operator. (English) Zbl 1114.30012
Summary: Let $${\mathcal S}_{\mathcal H}$$ denote the class of functions $$f=h+ \overline g$$ which are harmonic univalent and sense preserving in the unit disk $$U$$. Al-Shaqsi and Darus [On univalent functions with respect to $$K$$-symmetric points given by a generalised Ruscheweyh derivatives operator (to appear)] introduced a generalized Ruscheweyh derivatives operator denoted by $$D^n_\lambda$$ where $$D^n_\lambda f(z)=z+\sum^\infty_{k=2}[1+\lambda(k-1)]C(n,k) a_k z^k$$, where $$C(n,k)={k+n-1\choose n}$$. The authors, using this operators, introduce the class $${\mathcal H}^n_\lambda$$ of functions which are harmonic in $$U$$. Coefficient bounds, distortion bounds and extreme points are obtained.

##### MSC:
 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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