Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions

A. B.  Patil; T. G.  Shaba

doi:10.37863/umzh.v75i2.6602

A. B. Patil AISSMS College of Engineering, Pune, India
T. G. Shaba Landmark University, Omu-Aran, Nigeria

DOI: https://doi.org/10.37863/umzh.v75i2.6602

Keywords: Analytic function, Univalent function, Bi-univalent function, Starlike function, Bazilevic function, Fekete-Szego functional

Abstract

UDC 517.5

We introduce two new subclasses $\mathcal{U}_{\Sigma}(\alpha,\lambda)$ and ${\mathcal{B}_1}_{\Sigma}(\alpha)$ of analytic bi-univalent functions defined in the open unit disk $\mathbb{U}$, which are associated with the Bazilevich functions. In addition, for functions that belong to these subclasses, we obtain sharp bounds for the initial Taylor–Maclaurin coefficients $a_2$ and $a_3,$ as well as the sharp estimate for the Fekete–Szegö functional $a_3-\mu a_2^2.$

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