Search

In the current article, we introduce several new subclasses of m-fold symmetric analytic and bi-univalent functions associated with bounded boundary and bounded radius rotation within the open unit disk D. Utilizing the Faber polynomial expansion, we derive upper bounds for the coefficients | b m k + 1 | and establish initial coefficient bounds for | b m + 1 | and | b 2 m + 1 |. Additionally, we explore the Fekete–Szegö inequalities applicable to the functions that fall within these newly defined subclasses. [ABSTRACT FROM AUTHOR]

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]

In the present investigation, we introduce a new subclass of univalent functions F (u , λ) and a subclass of bi-univalent function F o , Σ (u , λ) with bounded boundary and bounded radius rotation. Some examples of the functions belonging to the classes F (u , λ) are also derived. For these new classes, the authors derive many interesting relations between these classes and the existing familiar subclasses in the literature. Furthermore, the authors establish new coefficient estimates for these classes. Apart from the above, the first two initial coefficient bounds for the class F o , Σ (u , λ) are established. [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]

In the current article, we introduce a new class of bi-close-to-convex functions with bounded boundary rotation. For this new class, the authors obtain the first three initial coefficient bounds of the newly defined bi-close-to-convex functions with bounded boundary rotation. By choosing special bi-convex functions, the authors obtain the first three initial coefficient bounds in the last section. The authors also verify the special cases where the familiar Brannan and Clunie's conjecture is satisfied. Furthermore, the famous Fekete–Szegö inequality is also obtained for this new class of functions. Apart from the new interesting results, some of the results presented here improves the earlier results existing in the literature. [ABSTRACT FROM AUTHOR]