Certain New Families for Bi-univalent Functions Defined by a Known Operator

다국어 초록 (Multilingual Abstract)

In this paper, we aim to introduce two new families of analytic and bi-univalent functionsassociated with the Attiya's operator, which is defined by the Hadamard product ofa 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-Szeg\"{o} 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.

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