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In this paper, a new subclass of bi-univalent functions linked to Lucas-Balancing polynomials is introduced. Bounds for the coefficients in the Taylor-Maclaurin series, denoted as |a2| and |a3|, are determined for these functions. The Fekete-Szegö functional problems are also addressed, and bounds for the second Hankel determinant for functions in this specific subclass are established. Additionally, it is shown that by adjusting the parameters in the main findings, several new results can be derived. [ABSTRACT FROM AUTHOR]

In this investigation, we present a new collection of analytic functions that includes Touchard polynomials. We then aim to calculate the Maclaurin coefficients |a2| and |a3| and address the Fekete-Szegö functional problem within this specific subfamily. Additionally, we demonstrate several new outcomes by specifying the parameters used in our main findings. [ABSTRACT FROM AUTHOR]

The aim of this study is to present novel collections of bi-univalent functions, which are characterized using the Bell Distribution. These collections are delineated through the application of Jacobi polynomials. We have established bounds for the Taylor-Maclaurin coefficients, particularly |a2| and |a3|. Additionally, we have investigated the Fekete-Szegö functional issues pertinent to functions within these subclasses. By concentrating on particular parameters in our principal findings, we have identified numerous new insights. [ABSTRACT FROM AUTHOR]

Making use of generalized bivariate Fibonacci polynomials, we propose two families of regular functions of the type ϕ (ζ) = ζ + ∑ j = 2 ∞ d j ζ j , which are bi-univalent in the disc { ζ ∈ C : | ζ | < 1 } involving the (p, q)-derivative operator. We find estimates on the coefficients | d 2 | , | d 3 | and the of Fekete–Szegö functional for members of these families. Relevant connections to the existing results and new consequences of the main result are presented. [ABSTRACT FROM AUTHOR]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This research investigates the second Hankel determinant for a specific class of functions associated with the Daehee polynomial. To achieve this, we introduce new subclasses of starlike functions in the context of Daehee polynomials. In complex analysis, establishing precise bounds for coefficient estimates in bi-univalent functions is essential, as these coefficients define the fundamental properties of conformal mappings. In this study, we derive sharp bounds for coefficient estimates within new subclasses of starlike functions related to Daehee polynomials, with most of the obtained limits demonstrating high accuracy. This work aims to inspire further exploration of rigorous bounds for analytic functions associated with innovative mapping domains. [ABSTRACT FROM AUTHOR]

This study defines three novel classes of bi‐univalent functions connected to generalized telephone numbers for the first time. We produced assessments about the Taylor–Maclaurin coefficients |a2| and |a3| and Fekete–Szegö functional problems for functions involving these novel subclasses for functions in every one regarding these three bi‐univalent function classes. Additional findings are anticipated to emerge after expertise the factors included in our significant outcomes, which have not yet been investigated by subordinating with generalized telephone numbers. [ABSTRACT FROM AUTHOR]

In this article, the strong class of bi-close-to-convex functions of order α and β in n-fold symmetric bi-univalent functions, which is the subclass of σ , is introduced. The upper bound value for a n + 1 , a 2 n + 1 for functions in these classes are obtained. Moreover, the Fekete–Szegö relation for our classes of functions are established. [ABSTRACT FROM AUTHOR]

In this paper, we make use of the generalized Sălăgean 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 D. The prime goal of this paper to derive sharp coefficient bounds in open unit disk D, especially the first two coefficient bounds for the functions belong to this class . The investigation also focuses on studying the classical Fekete-Szegö 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. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Qadisiyah Computer Science & Mathematics is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we present a novel class of Yamakawa-type bi-starlike functions. These functions are defined using Gegenbauer polynomials associated with q-calculus. We have derived estimates for the Maclaurin coefficients | a2 | and | a3 | for functions in the Yamakawa-type bi-starlike function subclass. Additionally, we have solved the Fekete-Szegö problems for functions in this new subclass. By specializing the parameters in our main results, we have obtained several new findings. [ABSTRACT FROM AUTHOR]

Copyright of Palestine Journal of Mathematics is the property of Palestine Polytechnic University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, we introduce and investigate a novel subclass of analytic biunivalent functions, which we define using Gegenbauer polynomials. We derive the initial coefficient bounds for |α2|, |α3|, and | α4|, and establish Fekete-Szegö inequalities for this class. In addition, we confirm that Brannan and Clunie's conjecture, |α2| ≤√2, is valid for this subclass. To facilitate better understanding, we provide visualizations of the functions, using appropriately chosen parameters. [ABSTRACT FROM AUTHOR]

By using the Mittag–Leffler function associated with functions of bounded boundary rotation, the authors introduce a few new subclasses of bi-univalent functions involving the Mittag–Leffler function with bounded boundary rotation in the open unit disk D. For these new classes, the authors establish initial coefficient bounds of | a 2 | and | a 3 | . Furthermore, the famous Fekete–Szegö coefficient inequality is also obtained for these new classes of functions. [ABSTRACT FROM AUTHOR]

In this paper, we conduct an investigation into a novel subclass of bi-univalent functions within the unit disk. The introduced subclass incorporates the generalized Srivastava-Attiya operator and satisfies specific quasi-subordination conditions. Through this study, the researchers determine the coefficient estimates |α2 | and |α3 | for functions within these subclasses and unveil new results by applying the operator to this particular subclass. The implications of these findings extend to complex analysis, number theory, and other branches of mathematics. Overall, this research significantly contributes to the theory of quasi-subordination of bi-univalent functions and enhances the understanding of the diverse applications of the Generalized Srivastava-Attiya Operator [ABSTRACT FROM AUTHOR]

In the present investigation, we consider new subclasses of Σρ consisting of regular and ρ-fold symmetric bi-univalent functions in the open unit disk. We obtain coefficient bounds for |aρ+1| and |a2ρ+3| of the functions from these new subclasses. [ABSTRACT FROM AUTHOR]

Our research introduces new subclasses of analytical functions that are defined by Euler polynomials. We then proceed to estimate the Fekete-Szegö functional problem and the Maclaurin coefficients for this specific subfamily, denoted as |a2| and |a3|. Furthermore, we demonstrate several new results that emerge when we specialize the parameters used in our main findings. [ABSTRACT FROM AUTHOR]

In this paper, we define a new class of bi-univalent functions of complex order ∑qn(τ, ς; φ) which is defined by subordination in the open unit disc D.By using DqnF(ς) operator. Furthermore, using the Faber polynomial expansions, we get upper bounds for the coefficients of function belonging to this class. [ABSTRACT FROM AUTHOR]

In this paper, we introduced two novel subclasses of bi-univalent functions, MΣ(α, B(x, ξ)) and HΣ(α, µ, B(x, ξ)), utilizing Lucas-Balancing polynomials. Within these function classes, we established bounds for the Taylor-Maclaurin coefficients |a2| and |a3|, addressing the Fekete-Szegö functional problems specific to functions within these new subclasses. Moreover, we illustrated how our primary findings could lead to various new outcomes through parameter specialization. [ABSTRACT FROM AUTHOR]

This study established upper bounds for the second and third coefficients of analytical and bi-univalent functions belonging to a family of particular classes of analytic functions utilizing q−Ultraspherical polynomials under q−Saigo’s fractional integral operator. We also discussed the Fekete-Szegö family function problem. As a result of the specialization of the parameters used in our main results, numerous novel outcomes were demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a novel type of analytic bi-univalent functions by utilizing specialized q-Salagean differential operators. Then, we use the q-analogue of the logarithmic function to introduce definition and provide properties of a class of bi-univalent functions. Further, we use the subordination principle to estimate the initial Taylor and Maclaurin coefficients for these given univalent functions. Additionally, we introduce new operators to demonstrate practical applications of the existing theory and establish Fakte-Szego results for each function in the defined sets. Further, we discuss certain coefficient inequalities in detail. [ABSTRACT FROM AUTHOR]

This study established upper bounds for the second and third coefficients of analytical and bi-univalent functions belonging to a family of particular classes of analytic functions utilizing $ q- $Ultraspherical polynomials under $ q- $Saigo's fractional integral operator. We also discussed the Fekete-Szegö family function problem. As a result of the specialization of the parameters used in our main results, numerous novel outcomes were demonstrated.

In this paper, we introduced two novel subclasses of bi-univalent functions, $ \mathcal{M}_{\Sigma}(\alpha, \mathcal{B}(x, \xi)) $ and $ \mathcal{H}_{\Sigma}(\alpha, \mu, \mathcal{B}(x, \xi)) $, utilizing Lucas-Balancing polynomials. Within these function classes, we established bounds for the Taylor-Maclaurin coefficients $ \left|a_2\right| $ and $ \left|a_3\right| $, addressing the Fekete-Szegö functional problems specific to functions within these new subclasses. Moreover, we illustrated how our primary findings could lead to various new outcomes through parameter specialization.

Estimates bounds for Carathéodory functions in the complex domain are applied to demonstrate sharp limits for the inverse of analytic functions. Determining these values is considered a more difficult task compared to finding the values of analytic functions themselves. The challenge lies in finding the sharp estimate for the functionals. While some recent studies have made progress in calculating the sharp boundary values of Hankel determinants associated with inverse functions, the Toeplitz determinant is yet to be addressed. Our research aims to estimate the determinants of the Toeplitz matrix, which is also linked to inverse functions. We also focus on computing these determinants for familiar analytical functions (pre-starlike, starlike, convex, symmetric-starlike) while investigating coefficient values. The study also provides an improvement to the estimation of the determinants of the pre-starlike class presented by Li and Gou.

Various researchers have considered different forms of bi-univalent functions in recent times, and this has continued to gain more attention in Geometric Function Theory (GFT), but not much study has been conducted in the area of application of the certain probability concept in geometric functions. In this manuscript, our motivation is the application of analytic and bi-univalent functions. In particular, the researchers examine bi-univalency of a generalized distribution series related to Bell numbers as a family of Caratheodory functions. Some coefficients of the class of the function are obtained. The results are new as far work on bi-univalency is concerned. [ABSTRACT FROM AUTHOR]

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

Bi-univalent functions associated with the leaf-like domain within the open unit disk 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 be not 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 | α 2 | and | α 3 | coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation. [ABSTRACT FROM AUTHOR]

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 | α 2 | and | α 3 | coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation. [ABSTRACT FROM AUTHOR]

We investigate some subclasses of regular and bi-univalent functions in the open unit disk that are associated with Lucas-Balancing polynomials in this work. For functions that belong to these subclasses, we obtain upper bounds on their initial coefficients. The Fekete–Szegö problem is also discussed. Along with presenting some new results, we also explore pertinent connections to earlier findings. [ABSTRACT FROM AUTHOR]

In this study, using the ideas of subordination and the quantum-difference operator, we established a new subclass S*(δ,σ, q) of q-starlike functions and the subclass S*σ (δ,σ, q) 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 S*(δ,σ, q), as well as sharp bounds for the inverse function h that belong to S*(δ,σ, q). We also investigated some results for the class of bi-univalent functions S*σ (δ,σ, q) and well-known corollaries were also highlighted to show connections between previous results and the findings of this paper. [ABSTRACT FROM AUTHOR]

The purpose of this study is to establish new subclasses within the function class ∑m, which consists of analytic as well as m-fold symmetric bi-univalent functions expressed within the open unit disk Q. Additionally, for functions belonging to each of the newly established subclasses, this paper establishes estimates with regards to the Taylor-Maclaurin coefficients given by |am+1| as well as |a2m+1| Moreover, we take into consideration of specific as well as existing special cases for our respective findings. [ABSTRACT FROM AUTHOR]

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.

On this study, two new subclasses of the function class $\Xi$ of bi-univalent functions of complex order defined in the open unit disc are introduced and investigated. These subclasses are connected to the Hohlov operator with $(\mathcal {P,Q})-$Lucas polynomial and meet subordinate criteria. For functions in these new subclasses, we also get estimates for the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. The results are also discussed as having a number of (old or new) repercussions.

In this article, we derive some estimates for the Taylor-Maclaurin coefficients of functions that belong to a new general subclass $ \Upsilon_\Sigma(\delta, \rho, \tau, n;\varphi) $ of bi-univalent functions in an open unit disk, which is defined by using the Ruscheweyh derivative operator and the principle of differential subordination between holomorphic functions. Our results are more accurate than the previous works and they generalize and improve some outcomes that have been obtained by other researchers. Under certain conditions, the derived bounds are smaller than those in the previous findings. Furthermore, if we specialize the parameters, several repercussions of this generic subclass will be properly obtained.

In this paper we introduce a new class of ϑ -bi-pseudo-starlike functions with respect to symmetric points associated with telephone numbers and determine the bounds of the initial Taylor–Maclaurin coefficients and the Fekete–Szegö problem for functions belonging to this class. Some special cases of main results presented here are stated which are new and give better improvement to the initial Taylor-Maclaurin coefficients. [ABSTRACT FROM AUTHOR]

In this study, we introduce a new class of normalized analytic and bi-univalent functions denoted by D Σ (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 D Σ (δ , η , λ , t , r) and derive upper bounds for the initial Taylor–Maclaurin coefficients | a 2 | and | a 3 | . Additionally, we establish connections between our results and previous research papers on this topic. [ABSTRACT FROM AUTHOR]

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 |α2| and |α3|. In this current work, the subfamily Fδ,qsc (α, Ξ) of bi-univalent functions in the sense of symmetric conjugate points with quasi subordination is defined. The Maclaurin coefficients |α2|, |α3| and besides related with these coefficients |α3 -- α2²| for functions belonging to this subfamily are derived. Further some corollaries are also presented. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc U = {z: z ∈ C and |z| < 1}. We find the bounds on the initial coefficients |c2| and |c3| and upper bounds for the Fekete-Szego functional for the functions in this class. [ABSTRACT FROM AUTHOR]

A bi-univalent function is a univalent function defined on the unit disc for which the inverse function has a univalent extension to the unit disc. In this paper, estimates for the initial as well as higher order coefficients |α4| and |α5| of bi-univalent functions belonging to certain class defined by subordination and of functions for which f and f −1 belong to different subclasses of univalent functions are derived. Generalization of existing known results were also pointed out. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new subclass of analytic and bi-univalent functions in the open unit disc $ U. $ For this subclass of functions, estimates of the initial coefficients $ \left\vert A_{2}\right\vert $ and $ \left\vert A_{3}\right\vert $ of the Taylor-Maclaurin series are given. An application of Legendre polynomials to this subclass of functions is presented. Furthermore, our study discusses several special cases.

In this paper, we introduce a new subclass of bi-univalent functions defined using Lucas-Balancing polynomials. For functions in each of these bi-univalent function subclasses, we derive estimates for the Taylor–Maclaurin coefficients a 2 and a 3 and address the Fekete–Szegö functional problems for functions belonging to this new subclass. We demonstrate that several new results can be derived by specializing the parameters in our main findings. The results obtained from this study will enrich the theoretical foundation of this field and open new avenues for mathematical inquiry and application. [ABSTRACT FROM AUTHOR]

In this article, we derive some estimates for the Taylor-Maclaurin coefficients of functions that belong to a new general subclass ΓΣ(δ, ρ, τ, η, φ) of bi-univalent functions in an open unit disk, which is defined by using the Ruscheweyh derivative operator and the principle of differential subordination between holomorphic functions. Our results are more accurate than the previous works and they generalize and improve some outcomes that have been obtained by other researchers. Under certain conditions, the derived bounds are smaller than those in the previous findings. Furthermore, if we specialize the parameters, several repercussions of this generic subclass will be properly obtained. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]