×

zbMATH — the first resource for mathematics

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.)
PDF BibTeX XML Cite
Full Text: EMIS EuDML