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In this article, using the Sǎlǎgean operator, we introduced three new subclasses of bi-univalent functions associated with bounded boundary rotation in open unit disk E. For these new classes, we first obtain initial Taylor-Maclaurin's coefficient bounds. Furthermore, the famous Fekete-Szegö inequality was also derived for these new subclass functions. Some improved results, when compared with those available in the literature, are also stated. [ABSTRACT FROM AUTHOR]

In the current article, the authors obtain Faber polynomial coefficient bounds for analytic bi-close-to-convex functions with bounded boundary rotation for two new subclasses. For these new classes, the authors estimate general coefficient bounds. Furthermore, the famous Fekete-Szegö inequality are also obtained for the newly defined subclasses of bi-univalent functions. [ABSTRACT FROM AUTHOR]

In this article, the authors use the Faber polynomial expansions to find the general coefficient estimates for a few new subclasses of bi-univalent functions with bounded boundary rotation and bounded radius rotation. Some of the results improve the existing coefficient bounds in the literature. [ABSTRACT FROM AUTHOR]

By using the Mittag–Leffler function associated with functions of bounded boundary rotation, the authors introduce a few new subclasses of bi-univalent functions involving the Mittag–Leffler function with bounded boundary rotation in the open unit disk D. For these new classes, the authors establish initial coefficient bounds of | a 2 | and | a 3 | . Furthermore, the famous Fekete–Szegö coefficient inequality is also obtained for these new classes of functions. [ABSTRACT FROM AUTHOR]

The objective of the present article is to introduce new subclasses of bi-Bazilevič functions, bi-quasi-convex functions and α -exponentially bi-convex functions involving functions with bounded boundary rotation of order ν. For the above-said newly defined classes, we obtain first two initial coefficient bounds. In addition, the familiar Fekete–Szegö coefficient inequality is too found for the newly introduced subclasses of bi-univalent functions. Apart from the new findings that are obtained, it also improves the prior estimates that are presented already in the literature. [ABSTRACT FROM AUTHOR]

In the current article, we introduced new subclasses of bi-univalent functions associated with bounded boundary rotation. For these new classes, the authors first obtained two initial coefficient bounds. They also verified the special cases where the familiar Brannan and Clunie's conjecture were satisfied. Furthermore, the famous Fekete-Szego inequality was obtained for the newly defined subclasses of bi-univalent functions, and some of the results improved the earlier results available in the literature. [ABSTRACT FROM AUTHOR]