Estimate for Initial MacLaurin Coefficients of Certain Subclasses of Bi-univalent Functions of Complex Order Associated with the Hohlov Operator

T. Bulboacă; G. Murugusundaramoorthy

Estimate for Initial MacLaurin Coefficients of Certain Subclasses of Bi-univalent Functions of Complex Order Associated with the Hohlov Operator

Complex Variables 2016-07-29 v1

Authors: T. Bulboacă , G. Murugusundaramoorthy

Abstract

In this paper we introduce and investigate two new subclasses of the function class $\Sigma$ of bi-univalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, and satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-MacLaurin coefficients $|a_2|$ and $|a_3|$ for functions in these new subclasses. Several known or new consequences of these results are also pointed out.

Keywords

bi-univalent functions complex order Hohlov operator initial MacLaurin coefficients Taylor-MacLaurin coefficients open unit disk subordination

Cite

@article{arxiv.1607.08285,
  title  = {Estimate for Initial MacLaurin Coefficients of Certain Subclasses of Bi-univalent Functions of Complex Order Associated with the Hohlov Operator},
  author = {T. Bulboacă and G. Murugusundaramoorthy},
  journal= {arXiv preprint arXiv:1607.08285},
  year   = {2016}
}

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