Initial Coefficients Upper Bounds for Certain Subclasses of Bi-Prestarlike Functions (original) (raw)

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.

Coefficient Inequalities for Certain Classes of Analytic and Univalent Functions

J. Ineq. Pure and Appl. Math

For functions f (z) which are starlike of order α, convex of order α, and λ-spirallike of order α in the open unit disk U, some interesting sufficient conditions involving coefficient inequalities for f (z) are discussed. Several (known or new) special cases and consequences of these coefficient inequalities are also considered.

Certain Inequalities for a General Class of Analytic and Bi-univalent Functions

In this work, the subclass S h,p Σ (λ, δ, γ) of the function class S of analytic and bi-univalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor-Maclaurin series of bi-univalent functions belonging this class are obtained. Also, some relevant classes are recognized and connections to previous results are made.

INITIAL COEFFICIENT BOUNDS FOR INTERESTING SUBCLASSES OF MEROMORPHIC AND BI-UNIVALENT FUNCTIONS

Journal of Mahani Mathematical Research, 2022

In this paper, we investigate an interesting subclass of univalent functions. Also, we introduce a new subclass of meromorphic bi-univalent functions. We obtain the estimates on the initial Taylor-Maclurin Coefficients for functions in the interesting subclass of meromorphically bi-univalent functions defined on ∆ = {z ∈ C : 1 < |z| < ∞}.

COEFFICIENT ESTIMATES FOR SOME SUBCLASSES OF ANALYTIC AND Bi-UNIVALENT FUNCTIONS

2017

In the present paper, we introduce and investigate two new subclasses BΣ(α, λ, μ) andMΣ(β, λ, μ) of bi-valent functions in the unit disk U. For functions belonging to the classes BΣ(α, λ, μ) andMΣ(β, λ, μ), we obtain bounds of the first two Taylor-Maclaurin coefficients of f(z).

Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions

2011

Estimates on the initial coefficients are obtained for normalized analytic functions fff in the open unit disk with fff and its inverse g=f−1g=f^{-1}g=f−1 satisfying the conditions that zf′(z)/f(z)zf'(z)/f(z)zf′(z)/f(z) and zg′(z)/g(z)zg'(z)/g(z)zg′(z)/g(z) are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made.

Convolutions of prestarlike functions

International Journal of Mathematics and Mathematical Sciences, 1983

The convolution of two functionsf(z)=∑n=0∞anznandg(z)=∑n=0∞bnzndefined as(f∗g)(z)=∑n=0∞anbnzn. Forf(z)=z−∑n=2∞anznandg(z)=z/(1−z)2(1−γ), the extremal function for the class of functions starlike of orderγ, we investigate functionsh, whereh(z)=(f∗g)(z), which satisfy the inequality|(zh′/h)−1|/|(zh′/h)+(1-2α)|<β,0≤α<1,0<β≤1for allzin the unit disk. Such functionsfare said to beγ-prestarlike of orderαand typeβ. We characterize this family in terms of its coefficients, and then determine extreme points, distortion theorems, and radii of univalence, starlikeness, and convexity. All results are sharp.