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Harmonic mappings related to the m-fold starlike functions

Author

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  • Aydoğan, Melike
  • Polatoğlu, Yaşar
  • Kahramaner, Yasemin

Abstract

In the present paper we will give some properties of the subclass of harmonic mappings which is related to m-fold starlike functions in the open unit disc D={z||z|<1}. Throughout this paper we restrict ourselves to the study of sense-preserving harmonic mappings. We also note that an elegant and complete treatment theory of the harmonic mapping is given in Durens monograph (Duren, 1983). The main aim of us to investigate some properties of the new class of us which represented as in the following form,S∗H(m)=f=h(z)+g(z)‾|f∈SH(m),g′(z)h′(z)≺b1p(z),h(z)∈S∗(m),p(z)∈P(m),where h(z)=z+∑n=1∞amn+1zmn+1, g(z)=∑n=0∞bmn+1zmn+1,|b1|<1.

Suggested Citation

  • Aydoğan, Melike & Polatoğlu, Yaşar & Kahramaner, Yasemin, 2015. "Harmonic mappings related to the m-fold starlike functions," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 805-809.
    • Handle: RePEc:eee:apmaco:v:267:y:2015:i:c:p:805-809
    DOI: 10.1016/j.amc.2014.10.016
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