The Fekete-Szegö problems for a subclass of m-fold symmetric bi-univalent functions (original) (raw)
Coefficient Related Studies for New Classes of Bi-Univalent Functions
Mathematics
Using the recently introduced Sălăgean integro-differential operator, three new classes of bi-univalent functions are introduced in this paper. In the study of bi-univalent functions, estimates on the first two Taylor–Maclaurin coefficients are usually given. We go further in the present paper and bounds of the first three coefficients a 2 , a 3 and a 4 of the functions in the newly defined classes are given. Obtaining Fekete–Szegő inequalities for different classes of functions is a topic of interest at this time as it will be shown later by citing recent papers. So, continuing the study on the coefficients of those classes, the well-known Fekete–Szegő functional is obtained for each of the three classes.
CERTAIN SUBCLASSES OF m-FOLD SYMMETRIC-SAKAGUCHI TYPE BI-UNIVALENT FUNCTIONS
2017
In this work, we introduce four new subclasses SΣm(α, λ, t), SΣm(β, λ, t), KΣm(α, λ, t) and KΣm(β, λ, t) of Σm consisting of analytic & m-fold symmetric bi-univalent functions in the open unit disk U. Furthermore for functions in each of the subclasses introduced in this paper, we obtain the initial coefficient bound for |am+1| and |a2m+1|. AMS Subject Classification: 30C45.
Mathematics
This paper presents a new general subfamily NΣmu,v(η,μ,γ,ℓ) of the family Σm that contains holomorphic normalized m-fold symmetric bi-univalent functions in the open unit disk D associated with the Ruscheweyh derivative operator. For functions belonging to the family introduced here, we find estimates of the Taylor–Maclaurin coefficients am+1 and a2m+1, and the consequences of the results are discussed. The current findings both extend and enhance certain recent studies in this field, and in specific scenarios, they also establish several connections with known results.
Coefficient Bounds for a Family of s-Fold Symmetric Bi-Univalent Functions
Axioms
We present a new family of s-fold symmetrical bi-univalent functions in the open unit disc in this work. We provide estimates for the first two Taylor–Maclaurin series coefficients for these functions. Furthermore, we define the Salagean differential operator and discuss various applications of our main findings using it. A few new and well-known corollaries are studied in order to show the connection between recent and earlier work.
Coefficient estimates for special subclasses of k-fold symmetric bi-univalent functions
Mathematics for Application, 2020
In the present paper, we consider two new subclasses N Σ k (µ, α, τ ) and N Σ k (µ, β, τ ) of Σ k consisting of analytic and k-fold symmetric bi-univalent functions defined in the open unit disc U = {z : z ∈ C and |z| < 1}. For functions belonging to the two classes introduced here, we derive their normalized forms. Furthermore, we find estimates of the initial coefficients |a k+1 | and |a 2k+1 | for these functions. Several related classes are also considered and connections to previously known results are made.
Estimates of Coefficient for Certain Subclasses of k-Fold Symmetric Bi-Univalent Functions
Iraqi Journal of Science
In the present paper, the authors introduce and investigates two new subclasses and, of the class k-fold bi-univalent functions in the open unit disk. The initial coefficients for all of the functions that belong to them were determined, as well as the coefficients for functions that belong to a field determining these coefficients requires a complicated process. The bounds for the initial coefficients and are contained among the remaining results in our analysis are obtained. In addition, some specific special improver results for the related classes are provided.
Initial Coefficient Bounds for Bi-Univalent Functions Related to Gregory Coefficients
Mathematics
In this article we introduce three new subclasses of the class of bi-univalent functions Σ, namely HGΣ, GMΣ(μ) and GΣ(λ), by using the subordinations with the functions whose coefficients are Gregory numbers. First, we evidence that these classes are not empty, i.e., they contain other functions besides the identity one. For functions in each of these three bi-univalent function classes, we investigate the estimates a2 and a3 of the Taylor–Maclaurin coefficients and Fekete–Szegő functional problems. The main results are followed by some particular cases, and the novelty of the characterizations and the proofs may lead to further studies of such types of similarly defined subclasses of analytic bi-univalent functions.