Class Of Bi-univalent Functions Research Articles

On the Study of Bi-Univalent Functions Defined by the Generalized S\u{a}l\u{a}gean Differential Operator

In this paper, we make use of the generalized S\u{a}l\u{a}gean differential operator to define a novel class of bi-univalent functions that is associated with the generalized hyperbolic sine function in the open unit disk $\mathbb{D}$. The prime goal of this paper to derive sharp coefficient bounds in open unit disk $\mathbb{D}$, especially the first two coefficient bounds for the functions belong to this class . The investigation also focuses on studying the classical Fekete-Szeg\"{o} functional problem for functions belong to this class. Furthermore, some known corollaries are highlighted based on the unique choices of the parameters involved in this class.

Bounds on Initial Coefficients for Bi-Univalent Functions Linked to q-Analog of Le Roy-Type Mittag-Leffler Function

This study introduces a new class of bi-univalent functions by incorporating the q-analog of Le Roy-type Mittag-Leffler functions alongside q-Ultraspherical polynomials. We formulate and solve the Fekete-Szegö functional problems for this newly defined class of functions, providing estimates for the coefficients |α2| and |α3| in their Taylor-Maclaurin series. Additionally, our investigation produces novel results by adapting the parameters in our initial discoveries.

Applications of q-Borel distribution series involving q-Gegenbauer polynomials to subclasses of bi-univalent functions

This study introduces a new class of bi-univalent functions in the open disk using q-Borel distribution series and q-Gegenbauer polynomials. It provides estimates for the Taylor coefficients |μ2| and |μ3| for this family of functions, as well as solutions for the Fekete-Szegö functional problems associated with this subclass. The study presents various innovative findings that result from the unique parameters used in the main results.

New Results on Coefficient Estimates for Different Classes of Bi-Univalent Functions

In the current work, we investigate two new subclasses and of class of bi-univalent functions found within the open unit disk . We derive the normalized forms of functions that belong to the two classes described above. Furthermore, we obtain estimates of the starting coefficients and for these functions. Multiple classifications are also taken into consideration, and connections to previously established findings are established.

Fekete-Szegö Inequality for a Subclass of Bi-Univalent Functions Linked to <i>q</i>-Ultraspherical Polynomials

In this study, we introduce a new class of bi-univalent functions using q-Ultraspherical polynomials. We derive the Fekete and Szegö functional problems for functions in this new subclass, as well as estimates for the Taylor-Maclaurin coefficients |α2| and |α3|. Furthermore, a collection of fresh outcomes is presented by customizing the parameters employed in our initial discoveries.

A Class of Bi-Univalent Functions in a Leaf-Like Domain Defined through Subordination via q̧-Calculus

Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q-calculus. The class is proved to not be empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on |α2| and |α3| coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation.

Second Hankel Determinant and Fekete–Szegö Problem for a New Class of Bi-Univalent Functions Involving Euler Polynomials

Second Hankel Determinant and Fekete–Szegö Problem for a New Class of Bi-Univalent Functions Involving Euler Polynomials

The Miller-Ross Poisson distribution and its applications to certain classes of bi-univalent functions related to Horadam polynomials

Within the scope of this research, we introduce a novel category of bi-univalent functions. Horadam polynomials are utilized to characterize these functions by utilizing series from the Poisson distribution of the Miller-Ross type. Functions from these new categories have been used to construct estimates for the Fekete-Szego functional, as well as estimates of the Taylor-Maclaurin coefficients |l2| and |l3|. These projections were created for the methods in each of these brand-new subclasses. We made some additional discoveries after, focusing on the traits that contributed to our initial findings.

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.

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.

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>

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.

Upper Estimates For Initial Coefficients and Fekete-Szegö Functional of A Class of Bi-univalent Functions Defined by Means of Subordination and Associated with Horadam Polynomials

In this work, a new class of bi-univalent functions \(I^{n+1}_{\Gamma_m,\lambda}(x,z)\) is defined by means of subordination. Upper bounds for some initial coefficients and the Fekete-Szegö functional of functions in the new class were obtained.

Certain Results on Subclasses of Analytic and Bi-Univalent Functions Associated with Coefficient Estimates and Quasi-Subordination

The purpose of the present paper is to introduce and investigate new subclasses of analytic function class of bi-univalent functions defined in open unit disks connected with a linear q-convolution operator, which are associated with quasi-subordination. We find coefficient estimates of h2, h3 for functions in these subclasses. Several known and new consequences of these results are also pointed out. There is symmetry between the results of the subclass fq,∑ μ(ζ,n,ρ,σ,ϑ,γ,δ,φ) and the results of the subclass ℵ∑q,δλ,ζ,n,ρ,σ,ϑ,φ.

On Rabotnov fractional exponential function for bi-univalent subclasses

Considering the interesting results obtained recently by studying Rabotnov function, a new investigation is presented in this paper related to the topic of introducing new classes of bi-univalent functions. Using the normalized Rabotnov function and the concept of subordination, a new class of bi-univalent functions [Formula: see text] is defined and studied regarding coefficient estimates. Bounds of the Taylor–Maclaurin coefficients [Formula: see text] and [Formula: see text] are given and using those estimates, Fekete–Szegö problem is also investigated for the newly introduced class. For particular values of the parameters involved in the definition of the class [Formula: see text], certain particular classes are obtained and investigated in the corollaries associated to each result proved for the class [Formula: see text].

Exploring a Special Class of Bi-Univalent Functions: q-Bernoulli Polynomial, q-Convolution, and q-Exponential Perspective

This research article introduces a novel operator termed q-convolution, strategically integrated with foundational principles of q-calculus. Leveraging this innovative operator alongside q-Bernoulli polynomials, a distinctive class of functions emerges, characterized by both analyticity and bi-univalence. The determination of initial coefficients within the Taylor-Maclaurin series for this function class is accomplished, showcasing precise bounds. Additionally, explicit computation of the second Hankel determinant is provided. These pivotal findings, accompanied by their corollaries and implications, not only enrich but also extend previously published results.

A New Pseudo-Type κ-Fold Symmetric Bi-Univalent Function Class

We introduce and study a new pseudo-type κ-fold symmetric bi-univalent function class that meets certain subordination conditions in this article. For functions in the newly formed class, the initial coefficient bounds are obtained. For members in this class, the Fekete–Szegö issue is also estimated. In addition, we uncover pertinent links to previous results and give a few observations.

Coefficient estimates for a class of bi-univalent functions involving Mittag-Leffler type Borel distribution

Coefficient estimates for a class of bi-univalent functions involving Mittag-Leffler type Borel distribution

Certain New Applications of Faber Polynomial Expansion for a New Class of bi-Univalent Functions Associated with Symmetric q-Calculus

In this study, we applied the ideas of subordination and the symmetric q-difference operator and then defined the novel class of bi-univalent functions of complex order γ. We used the Faber polynomial expansion method to determine the upper bounds for the functions belonging to the newly defined class of complex order γ. For the functions in the newly specified class, we further obtained coefficient bounds ρ2 and the Fekete–Szegő problem ρ3−ρ22, both of which have been restricted by gap series. We demonstrate many applications of the symmetric Sălăgean q-differential operator using the Faber polynomial expansion technique. The findings in this paper generalize those from previous studies.