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The Youngnam Mathematical Society (영남수학회)
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CERTAIN NEW FAMILIES FOR BI-UNIVALENT FUNCTIONS DEFINED BY A KNOWN OPERATOR

  • Received : 2021.05.03
  • Accepted : 2021.05.31
  • Published : 2021.05.31
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Abstract

In this paper, we aim to introduce two new families of analytic and bi-univalent functions associated with the Attiya's operator, which is defined by the Hadamard product of a generalized Mittag-Leffler function and analytic functions on the open unit disk. Then we estimate the second and third coefficients of the Taylor-Maclaurin series expansions of functions belonging to these families. Also, we investigate Fekete-Szegö problem for these families. Some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out. Two naturally-arisen problems are given for further investigation.

Keywords

Acknowledgement

The authors are very and really grateful to the anonymous referees for their constructive and detailed comments which improved this paper.

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