Symmetric Bi-univalent Functions Research Articles

Maclaurin Coefficients Estimates for New classes of m-Fold Symmetric Bi-Univalent Functions

The purpose of this study is to establish new subclasses within the function class , which consists of analytic as well as -fold symmetric bi-univalent functions expressed within the open unit disk . Additionally, for functions belonging to each of the newly established subclasses, this paper establishes estimates with regards to the Taylor-Maclaurin coefficients given by as well as . Moreover, we take into consideration of specific as well as existing special cases for our respective findings.

Bounds on the Initial Coefficients for New Subclasses of m-Fold Symmetric Bi-univalent Functions

The aim from this study is to propose and explore two new classes and of made up of bi-univalent functions that are m-fold symmetric and analytic which are defined within the unit disk that is open. For each functions that correspond to these subclasses we derive upper bounds for the coefficients and . Many of the newly discovered and well-known outcomes are demonstrated to be special cases of our findings.

Two Families of m-fold Symmetric Bi-univalent Functions Involving a Linear Combination of Bazilevic Starlike and Convex Functions

In the present paper, we define two new families $K M_{\Sigma_m}(\lambda, \gamma, \delta ; \alpha)$ and $K M_{\Sigma_m}^*(\lambda, \gamma, \delta ; \beta)$ of holomorphic and m-fold symmetric bi-univalent functions associated with the Bazilevic starlike and convex functions in the open unit disk U. We find upper bounds for the first two Taylor-Maclaurin $\left|a_{m+1}\right|$ and $\left|a_{2 m+1}\right|$ for functions in these families. Further, we point out several special cases for our results.

Note on bounds on the coefficients of a subclass of m-fold symmetric bi-univalent functions

Abstract In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions which both f ⁢ ( z ) {f(z)} and f - 1 ⁢ ( z ) {f^{-1}(z)} are m-fold symmetric on the open unit disk. Furthermore, we find upper bounds for the initial coefficients | a m + 1 | {|a_{m+1}|} and | a 2 ⁢ m + 1 | {|a_{2m+1}|} for functions in this subclass. The results presented in this paper generalize and improve some recent works

Hankel determinant for a general subclass of m-fold symmetric biunivalent functions defined by Ruscheweyh operators

Making use of the Hankel determinant and the Ruscheweyh derivative, in this work, we consider a general subclass of m-fold symmetric normalized biunivalent functions defined in the open unit disk. Moreover, we investigate the bounds for the second Hankel determinant of this class and some consequences of the results are presented. In addition, to demonstrate the accuracy on some functions and conditions, most general programs are written in Python V.3.8.8 (2021).

Coefficient Bounds for a New Families of m-Fold Symmetric Bi-Univalent Functions Defined by Bazilevic Convex Functions

In this paper, we find upper bounds for the first two Taylor-Maclaurin $\left|a_{m+1}\right|$ and $\left|a_{2m+1}\right|$ for two new families $L_{\Sigma_m}(\delta, \gamma ; \alpha)$ and $L_{\Sigma_m}^{*}(\delta, \gamma ; \alpha)$ of holomorphic and $m$-fold symmetric bi-univalent functions associated with the Bazilevic convex functions defined in the open unit disk $U$. Further, we point out several certain special cases for our results.

A Family of Holomorphic and m-Fold Symmetric Bi-Univalent Functions Endowed with Coefficient Estimate Problems

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 Estimates for a General Subclass of m-fold Symmetric Bi-univalent Functions by Using Faber Polynomials

Coefficient Estimates for a General Subclass of m-fold Symmetric Bi-univalent Functions by Using Faber Polynomials

Coefficient Bounds for a Family of s-Fold Symmetric Bi-Univalent Functions

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.

On the Hankel Determinant of m-fold Symmetric Bi-Univalent Functions Using a New Operator

In this article, we aim to describe a new operator J_(s,a,μ)^(δ,λ) via convolution. Moreover, we aim to present a new subclass C_Σm (τ;β) related to m-fold symmetric bi-univalent functions in the open unit disk Θ={z∈C∶|z| ˂ 1 }. Finally, an estimate related to the Hankel determinant for functions in C_Σm (τ;β) are given.

The study of coefficient estimates and Fekete–Szegö inequalities for the new classes of m-fold symmetric bi-univalent functions defined using an operator

The objective of this paper is to introduce new classes of m-fold symmetric bi-univalent functions. We discuss estimates on the Taylor–Maclaurin coefficients |a_{m+1}| and |a_{2m+1}|, and the Fekete–Szegő problem is also considered for the new classes of functions introduced. We denote these classes by MF-S_{Sigma ,m}^{p,q}(h), MF-S_{Sigma , m}^{p,q}(s), and MF-S_{Sigma , m}^{b,d}. Quantum calculus aspects are also considered in this study to enhance its novelty and to obtain more interesting results.

Certain new applications of Faber polynomial expansion for some new subclasses of $ \upsilon $-fold symmetric bi-univalent functions associated with $ q $-calculus

<abstract><p>In this article, we define the $ q $-difference operator and Salagean $ q $-differential operator for $ \upsilon $-fold symmetric functions in open unit disk $ \mathcal{U} $ by first applying the concepts of $ q $-calculus operator theory. Then, we considered these operators in order to construct new subclasses for $ \upsilon $-fold symmetric bi-univalent functions. We establish the general coefficient bounds $ |a_{\upsilon k+1}| $ for the functions in each of these newly specified subclasses using the Faber polynomial expansion method. Investigations are also performed on Feketo-Sezego problems and initial coefficient bounds for the function $ h $ that belong to the newly discovered subclasses. To illustrate the relationship between the new and existing research, certain well-known corollaries of our main findings are also highlighted.</p></abstract>

Several Subclasses of r-Fold Symmetric Bi-Univalent Functions possess Coefficient Bounds

In this paper we offer two new subclasses of an open unit disk of r-fold symmetric bi-univalent functions. The Taylor-Maclaurin coefficients have their coefficient bounds calculated. Furthermore, for functions in , we have solved Fekete- functional issues. For the applicable classes, there are also a few particular special motivator results.

Maclaurin Coefficient Estimates for a New Subclasses of m-Fold Symmetric Bi-Univalent Functions

In this paper, we obtain upper bounds for the first two Taylor-Maclaurin and for two new families Υ_(Σ_m ) (η,γ;α) and Υ_(Σ_m)^* (η,γ;β) of holomorphic and m-fold symmetric bi-univalent functions defined in the open unit disk U. Further, we point out several certain special cases for our results.

On τ-Pseudo-ν-Convex κ-Fold Symmetric Bi-Univalent Function Family

The object of this article is to explore a τ-pseudo-ν-convex κ-fold symmetric bi-univalent function family satisfying subordinations condition generalizing certain previously examined families. We originate the initial Taylor–Maclaurin coefficient estimates of functions in the defined family. The classical Fekete–Szegö inequalities for functions in the defined τ-pseudo-ν-convex family is also estimated. Furthermore, we present some of the special cases of the main results. Relevant connections with those in several earlier works are also pointed out. Our study in this paper is also motivated by the symmetry nature of κ-fold symmetric bi-univalent functions in the defined class.

Applications of q-Symmetric Derivative Operator to the Subclass of Analytic and Bi-Univalent Functions Involving the Faber Polynomial Coefficients

In this paper, using the basic concepts of symmetric q -calculus operator theory, we define a symmetric q -difference operator for m -fold symmetric functions. By considering this operator, we define a new subclass ℛ b φ , m , q of m -fold symmetric bi-univalent functions in open unit disk U . As in applications of Faber polynomial expansions for f m ∈ ℛ b φ , m , q , we find general coefficient a m k + 1 for n ≥ 4 , Fekete–Szegő problems, and initial coefficients a m + 1 and a 2 m + 1 . Also, we construct q -Bernardi integral operator for m -fold symmetric functions, and with the help of this newly defined operator, we discuss some applications of our main results. For validity of our result, we have chosen to give some known special cases of our main results in the form of corollaries and remarks.

Coefficient Estimates for Subclass of m-Fold Symmetric Bi- Univalent Functions

In the present paper, a general subclass Mh,p Σm (λ, γ) of the m-Fold symmetric bi-univalent functions is deĄned. Also, the estimates of the TaylorMaclaurin coefficients |am+1|, |a2m+1| and Fekete-Szegö problems are obtained for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.

A Special Family of m-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition

In this paper, we introduce a special family Mσm(τ,ν,η,φ) of the function family σm of m-fold symmetric bi-univalent functions defined in the open unit disc D and obtain estimates of the first two Taylor–Maclaurin coefficients for functions in the special family. Further, the Fekete–Szegö functional for functions in this special family is also estimated. The results presented in this paper not only generalize and improve some recent works, but also give new results as special cases.

Fekete–Szegö Functional Problem for a Special Family of m-Fold Symmetric Bi-Univalent Functions

In the current work, we introduce a special family of the function family of analytic and m-fold symmetric bi-univalent functions and obtain estimates of the Taylor–Maclaurin coefficients |dm+1| and |d2m+1| for functions in the special family. For δ a real number, Fekete–Szegö functional |d2m+1−δdm+12| for functions in the special family is also estimated. We indicate several cases of the defined family and connections to existing results are also discussed.

Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m-Fold Symmetric Bi-Univalent Functions

The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin coefficients |am+1| and |a2m+1| are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes.