Coefficient Bounds for a subclass of bi-prestarlike functions associated with the Chebyshev Polynomials (original) (raw)
Related papers
Coefficient Bounds for Subclasses of Biunivalent Functions Associated with the Chebyshev Polynomials
We introduce and investigate new subclasses of biunivalent functions defined in the open unit disk, involving Sȃlȃgean operator associated with Chebyshev polynomials. Furthermore, we find estimates of the first two coefficients of functions in these classes, making use of the Chebyshev polynomials. Also, we give Fekete-Szegö inequalities for these function classes. Several consequences of the results are also pointed out.
On sharp Chebyshev polynomial bounds for a general subclass of bi-univalent functions
2021
In the present paper, we introduce a subclass BΣ (ν, σ, ρ) of the bi-univalent function class Σ, which is defined in the open unit disk U using the Chebyshev polynomials along with subordination. Further, we obtain sharp bounds for the initial coefficients a2, a3 and the Fekete-Szegö functional a3 − δa2 for the functions belong to this subclass. M.S.C. 2010: 30C45, 30C50.
Initial Coefficients Upper Bounds for Certain Subclasses of Bi-Prestarlike Functions
Axioms
In this article, we introduce and study the behavior of the modules of the first two coefficients for the classes NΣ(γ,λ,δ,μ;α) and NΣ*(γ,λ,δ,μ;β) of normalized holomorphic and bi-univalent functions that are connected with the prestarlike functions. We determine the upper bounds for the initial Taylor–Maclaurin coefficients |a2| and |a3| for the functions of each of these families, and we also point out some special cases and consequences of our main results. The study of these classes is closely connected with those of Ruscheweyh who in 1977 introduced the classes of prestarlike functions of order μ using a convolution operator and the proofs of our results are based on the well-known Carathédory’s inequality for the functions with real positive part in the open unit disk. Our results generalize a few of the earlier ones obtained by Li and Wang, Murugusundaramoorthy et al., Brannan and Taha, and could be useful for those that work with the geometric function theory of one-variable...
Advances on the coefficients of bi-prestarlike functions
Comptes Rendus Mathematique, 2016
Since 1923, when Löwner proved that the inverse of the Koebe function provides the best upper bound for the coefficients of the inverses of univalent functions, finding sharp bounds for the coefficients of the inverses of subclasses of univalent functions turned out to be a challenge. Coefficient estimates for the inverses of such functions proved to be even more involved under the bi-univalency requirement. In this paper, we use the Faber polynomial expansions to find upper bounds for the coefficients of bi-prestarlike functions and consequently advance some of the previously known estimates. Published by Elsevier Masson SAS on behalf of Académie des sciences. r é s u m é Depuis 1923, lorsque Löwner a montré que l'inverse de la fonction de Koebe fournit la majoration optimale pour les coefficients des inverses des fonctions univalentes, s'est posé le défi de trouver des bornes fines pour les coefficients des inverses de fonctions univalentes dans certaines classes. Ce problème s'est révélé être encore plus intriqué sous la condition de bi-univalence. Utilisant les développements de polynômes de Faber pour les coefficients des fonctions bi-pré-étoilées, nous améliorons dans cette Note quelques estimations déjà connues. Published by Elsevier Masson SAS on behalf of Académie des sciences.
Boletín de la Sociedad Matemática Mexicana, 2019
Our objective in this paper is to introduce and investigate a newly-constructed subclass of normalized analytic and bi-univalent functions by means of the Chebyshev polynomials of the second kind. Upper bounds for the second and third Taylor-Maclaurin coefficients, and also Fekete-Szegö inequalities of functions belonging to this subclass are founded. Several connections to some of the earlier known results are also pointed out.