Bi-univalent Functions Research Articles

Fekete-Szegö type functionals associated with certain subclasses of bi-univalent functions

In this article, we define and discuss some new subclasses of bi-univalent functions associated with Fibonacci numbers and shell-like curves. We estimate the first two Taylor-Maclaurin coefficients for functions belonging to these classes. We study the inequalities related with Fekete-Szegö type. Furthermore, we point out some corollaries related to existing result.

Initial Coefficient Bounds Analysis for Novel Subclasses of Bi-Univalent Functions linked with Horadam Polynomials

In this work, we investigate some subclasses of bi-univalent and regular functions associated with Horadam polynomials in the open unit disk $\mathfrak{U}=\{\varsigma\in\mathbb{C}:|\varsigma| <1\}$. For functions that belong to these subclasses, we find bounds on their initial coefficients. The functional problem of Fekete-Szegö is also examined. Along with presenting some new results, we also talk about pertinent connections to earlier findings.

Initial Coefficient Bounds Analysis for Novel Subclasses of Bi-Univalent Functions linked with Horadam Polynomials

In this work, we investigate some subclasses of bi-univalent and regular functions associated with Horadam polynomials in the open unit disk $\mathfrak{U}=\{\varsigma\in\mathbb{C}:|\varsigma| <1\}$. For functions that belong to these subclasses, we find bounds on their initial coefficients. The functional problem of Fekete-Szegö is also examined. Along with presenting some new results, we also talk about pertinent connections to earlier findings.

"A New Subclass of Bi-Univalent Functions Associated with Balancing Polynomial"

"A New Subclass of Bi-Univalent Functions Associated with Balancing Polynomial"

Coefficient bounds and second Hankel determinant for a subclass of symmetric bi-starlike functions involving Euler polynomials

Various operators of fractional calculus, as well as their quantum (or q-) extensions have been used widely and successfully in the study of the Taylor-Maclaurin coefficient estimation problems for many different families of normalized analytic, univalent and bi-univalent functions in Geometric Function Theory of Complex Analysis. On the other hand, Numerous writers have extensively employed orthogonal polynomials in the framework of Geometric Function Theory in Complex analysis. The recent and ongoing studies on this topic is primarily what drives us. In this paper, we solve the Fekete-Szegö problem for the symmetric function classes of analytical and bi-univalent functions involving the Euler polynomials. We also give estimates for the coefficients and an upper bound for the second Hankel determinant.

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.

On Third Hankel Determinant for Certain Subclass of Bi-Univalent Functions

This study presents a subclass S(β) of bi-univalent functions within the open unit disk region D. The objective of this class is to determine the bounds of the Hankel determinant of order 3, (Ⱨ3(1)). In this study, new constraints for the estimates of the third Hankel determinant for the class S(β) are presented, which are of considerable interest in various fields of mathematics, including complex analysis and geometric function theory. Here, we define these bi-univalent functions as S(β) and impose constraints on the coefficients │an│. Our investigation provides the upper bounds for the bi-univalent functions in this newly developed subclass, specifically for n = 2, 3, 4, and 5. We then derive the third Hankel determinant for this particular class, which reveals several intriguing scenarios. These findings contribute to the broader understanding of bi-univalent functions and their potential applications in diverse mathematical contexts. Notably, the results obtained may serve as a foundation for future investigations into the properties and applications of bi-univalent functions and their subclasses.

A New Method for Estimating General Coefficients to Classes of Bi-univalent Functions

This study establishes a new method to investigate bounds of ak; k≥n, for certain general classes of bi-univalent functions. The results include a number of improvements and generalizations for well-known estimations. We also discuss bounds of nan2−a2n−1 and consider several corollaries, remarks, and consequences of the results presented in this paper.

On a Certain Class of Bi-Univalent Functions in Connection with Gegenbauer Polynomials

Recent direction of studies shows that there is a kin connection between regular functions and orthogonal polynomials. In this paper, we study a new class of regular and bi-univalent functions that involve the familiar Gegenbauer polynomials. Some achieved results include some early coefficient bounds and the upper estimates for the Fekete-Szegö inequalities with real and complex parameters.

Applications of Horadam Polynomials for Bazilevič and λ-Pseudo-Starlike Bi-Univalent Functions Associated with Sakaguchi Type Functions

In this study, we introduce a new class of normalized analytic and bi-univalent functions denoted by DΣ(δ,η,λ,t,r). These functions are connected to the Bazilevič functions and the λ-pseudo-starlike functions. We employ Sakaguchi Type Functions and Horadam polynomials in our survey. We establish the Fekete-Szegö inequality for the functions in DΣ(δ,η,λ,t,r) and derive upper bounds for the initial Taylor–Maclaurin coefficients |a2| and |a3|. Additionally, we establish connections between our results and previous research papers on this topic.

Faber polynomial coefficient inequalities for bi-Bazilevič functions associated with the Fibonacci-number series and the square-root functions

Two new subclasses of the class of bi-Bazilevič functions, which are related to the Fibonacci-number series and the square-root functions, are introduced and studied in this article. Under a special choice of the parameter involved, these two classes of Bazilevič functions reduce to two new subclasses of star-like biunivalent functions related with the Fibonacci-number series and the square-root functions. Using the Faber polynomial expansion (FPE) technique, we find the general coefficient bounds for the functions belonging to each of these classes. We also find bounds for the initial coefficients for bi-Bazilevič functions and demonstrate how unexpectedly these initial coefficients behave in relation to the square-root functions and the Fibonacci-number series.

Fekete-Szegö Functional of a Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials

In this paper, we introduce and investigate a class of bi-univalent functions, denoted by $\mathcal{F}(n, \alpha, \beta)$, that depends on the Ruscheweyh operator. For functions in this class, we derive the estimations for the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. Moreover, we obtain the classical Fekete-Szeg\"{o} inequality of functions belonging to this class.

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 of Bi-Univalent Function Involving Pseudo-Starlikeness Associatedwith Sigmoid Function Defined by Salagean Operator via Chebyshev Polynomial

Some special classes of univalent functions play an important role in geometric function theory because of their geometric properties. Many of such classes have been introduced and studied; some became well known, for example, the classes of convex, starlike, close to convex, strongly convex and strongly starlike functions. Previous studies by Awolere and Oladipupo (2018) now served as motivation and background to investigate certain classes of analytic, univalent and bi-univalent functions in terms of their coefficient bounds involving salagean and sigmoid functions via Chebyshev poynomial. The classes 퐻푛(휆,훽,훾(푠),휙(푧,푡))are newly established classes for which coefficient bounds will be determined. The aim of the present work is to investigate coefficient bound for class 퐻푛(휆,훽,훾(푠),휙(푧,푡))of pseudo-starlikeness associated with sigmoid functions defined by Salagean operator via Chebyshev polynomial, Fekete-szego problem will also be established and the Hankel of the function will be determined

On bi-univalent functions of quasi-subordination associated with convolution operator

Within the open unit disk, the work presents a novel subclass of bi-univalent functions. The generalized derived operator and the differential operator are convolved to produce this subclass, which meets the quasi-subordination criterion. The paper also calculates the coefficient estimates for |a2| and |a3|this subclass. Furthermore, the two operators are applied to the subclass, resulting in new findings.

Study of quantum calculus for a new subclass of $ q $-starlike bi-univalent functions connected with vertical strip domain

<abstract><p>In this study, using the ideas of subordination and the quantum-difference operator, we established a new subclass $ \mathcal{S} ^{\ast }\left(\delta, \sigma, q\right) $ of $ q $-starlike functions and the subclass $ \mathcal{S}_{\Sigma }^{\ast }\left(\delta, \sigma, q\right) $ of $ q $-starlike bi-univalent functions associated with the vertical strip domain. We examined sharp bounds for the first two Taylor-Maclaurin coefficients, sharp Fekete-Szegö type problems, and coefficient inequalities for the function $ h $ that belong to $ \mathcal{S}^{\ast }\left(\delta, \sigma, q\right) $, as well as sharp bounds for the inverse function $ h $ that belong to $ \mathcal{S}^{\ast }\left(\delta, \sigma, q\right) $. We also investigated some results for the class of bi-univalent functions $ \mathcal{S}_{\Sigma }^{\ast }\left(\delta, \sigma, q\right) $ and well-known corollaries were also highlighted to show connections between previous results and the findings of this paper.</p></abstract>

Applications Poisson Distribution and Ruscheweyh Derivative Operator for Bi-Univalent Functions

In this paper we establish upper bounds for the second and third coefficients of holomorphic and bi-univalent functions in a new family which involve the Bazilevič functions and β-pseudo-starlike functions under a new operator joining Poisson distribution with Ruscheweyh derivative operator. Also, we discuss Fekete-Szegö problem of functions in this family.

Novel classes of bi-univalent functions of the Sălăgean type with a modified sigmoid unit action function

In this work, used (β, ζ)-Lucas polynomials that involve the modified sigmoid activation function ψ(δ) to develop a family of analytic functions along with Sălăgeantype bi-univalent functions. And obtain upper bounds for functions that belong to these subclasses. Furthermore, Fekete-Szegö inequality for these families is discussed.

Quasi subordinations for bi-univalent functions with symmetric conjugate points

Many researchers have recently acquainted and researched several interesting subfamilies of bi-univalent function family δ and they have found non-sharp estimates on the first two Taylor-Maclaurin coefficients |a_2 | and |a_3 |. In this current work, the subfamily F_(δ,q)^sc (α,Ξ) of bi-univalent functions in the sense of symmetric conjugate points with quasi subordination is defined. The Maclaurin coefficients |a_2 |, |a_3 | and besides related with these coefficients |a_3-〖a_2〗^2 | for functions belonging to this subfamily are derived. Further some corollaries are also presented.