Geodesic
On harmonic univalent functions defined by a~generalized Ruscheweyh derivatives operator
Lobachevskii journal of mathematics, Tome 22 (2006), pp. 19-26.

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Let $\mathcal{S_H}$ denote the class of functions $f=h+\overline g$ which are harmonic univalent and sense preserving in the unit disk $\mathbf U$. Al-Shaqsi and Darus [7] introduced a generalized Ruscheweyh derivatives operator denoted by $D^n_\lambda$ where $D^n_\lambda f(z)=z+\sum\limits_{k=2}^\infty[1+\lambda(k-1)]C(n,k)a_kz^k$, 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 $\mathbf U$. Coefficient bounds, distortion bounds and extreme points are obtained.
Keywords: univalent functions, Harmonic functions, derivative operator. 
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M. Darus; Kh. al-Shaqsi. On harmonic univalent functions defined by a~generalized Ruscheweyh derivatives operator. Lobachevskii journal of mathematics, Tome 22 (2006), pp. 19-26. http://geodesic.mathdoc.fr/item/LJM_2006_22_a2/

[1] S. Ruscheweyh, “New criteria for univalent functions”, Proc. Amer. Math. Soc., 49 (1975), 109–115 | DOI | MR | Zbl

[2] J. Clunie and T. Shell-Small, “Harmonic univalent functions”, Ann. Acad. Aci. Fenn. Ser. A I Math., 9 (1984), 3–25 | MR | Zbl

[3] H. Silverman, “Harmonic univalent functions with negative coefficients”, Proc. Amer. Math. Soc., 51 (1998), 283–289 | MR

[4] H. Silverman and E. M. Silvia, “Subclasses of harmonic univalent functions”, New Zeal. J. Math., 28 (1999), 275–284 | MR | Zbl

[5] J. M. Jahangiri, “Harmonic functions starlike in the unite disk”, J. Math. Anal. Appl., 235 (1999), 470–477 | DOI | MR | Zbl

[6] S. Yalçin and M. Öztürk, “A new subclass of complex harmonic functions”, Math. Ineq. Appl., 7 (2004), 55–61 | MR | Zbl

[7] K. Al Shaqsi and M. Darus, “On univalent functions with respect to $K$-symmetric points given by a generalised Ruscheweyh derivatives operator” (to appear)