TY - JOUR
AU - A. B. Patil
AU - T. G. Shaba
PY - 2023/03/02
Y2 - 2023/04/01
TI - Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 75
IS - 2
SE - Research articles
DO - 10.37863/umzh.v75i2.6602
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/6602
AB - UDC 517.5We 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 $a_3-\mu a_2^2.$
ER -