Taylor-Maclaurin Coefficients Research Articles

Subclasses of Bi-Univalent Functions Connected with Caputo-Type Fractional Derivatives Based upon Lucas Polynomial

In the current paper, we introduce new subclasses of analytic and bi-univalent functions involving Caputo-type fractional derivatives subordinating to the Lucas polynomial. Furthermore, we find non-sharp estimates on the first two Taylor–Maclaurin coefficients a2 and a3 for functions in these subclasses. Using the values of a2 and a3, we determined Fekete–Szegő inequality for functions in these subclasses. Moreover, we pointed out some more subclasses by fixing the parameters involved in Lucas polynomial and stated the estimates and Fekete–Szegő inequality results without proof.

Coefficients Estimates for New Subclasses of Bi-univalent Functions Using Convolution Operator

We offered and suggested some classes N_(Ω,b,α,γ)^(μ,δ) (ψ,τ,φ) and C_(Ω,b,α,γ)^(μ,δ) (τ,a,ψ,φ) of bi-univalent functions in the unit disk υ, to apply the effects to the classes through convolution of the operators R_q^δ f(z) and I_(s,a,µ)^λ f(z). Which satisfies the condition quasi-subordination. We got estimates the first two Taylor-Maclaurin coefficients |a_2 | and |a_3 | by convolution of the operators R_q^δ f(z) and I_(s,a,µ)^λ f(z) .

Results on New Subclasses for Bi-Univalent Functions Using Quasi-Subordination

The present study introduces and examines two specific subclasses, and of bi-univalent functions that are defined by quasi-subordination. We obtain approximations for the Taylor-Maclaurin coefficients and for functions within these subclasses.

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.

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.

An application of the Mittag-Leffler-type Borel distribution and Gegenbauer polynomials on a certain subclass of bi-univalent functions

The Mittag-Leffler-type Borel distribution is widely recognized and utilized as a beneficial and pertinent model across numerous applications. This study presents a new subclass of normalized analytic bi-univalent functions that combines Gegenbauer polynomials and the Mittag-Leffler-type Borel distribution. Employing this subclass enables us to derive novel approximations for Taylor-Maclaurin coefficients, |a2| and |a3|, as well as delve into the investigation of the Fekete-Szegö functional. Additionally, we explore a variety of new findings that arise through the specialization of parameters in our primary results.

On α-Pseudo Spiralike Functions Associated with Exponential Pareto Distribution (EPD) and Libera Integral Operator

The present study aims at investigating some characterizations of a new subclass Gα(μ,τ) and obtaining the bounds on the first two Taylor–Maclaurin coefficients for functions belonging to the newly introduced subclass. In order to achieve this, a compound function Lx,nσ(z) is derived from the convolution of the analytic function f(z) and a modified exponential Pareto distribution G(x) in conjunction with the famous Libera integral operator L(ζ). With the aid of the derived function, the aforementioned subclass Gα(μ,τ) is introduced, while some properties of functions belonging to this subclass are considered in the open unit disk.

Coefficient estimates for a subclass of bi-univalent functions associated with the Salagean differential operator

In this paper, we present and examine a novel subset of the function class ∑, which consists of analytic and bi-univalent functions defined in the open unit disk U and connected to the Salagean differential operator. Additionally, we determine estimates for the Taylor-Maclaurin coefficients |a2| and |a3| functions within this new subclass and enhance some recent findings. 2010 Mathematics Subject Classification. 30C45; 30C50.

Some m-fold symmetric bi-univalent function classes and their associated Taylor-Maclaurin coefficient bounds

The Ruscheweyh derivative operator is used in this paper to introduce and investigate interesting general subclasses of the function class Σm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\Sigma_{m}$\\end{document} of m-fold symmetric bi-univalent analytic functions. Estimates of the initial Taylor-Maclaurin coefficients |am+1|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\vert a_{m+1} \\vert $\\end{document} and |a2m+1|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\vert a_{2 m+1} \\vert $\\end{document} are obtained for functions of the subclasses introduced in this study, and the consequences of the results are discussed. Additionally, the Fekete-Szegö inequalities for these classes are investigated. The results presented could generalize and improve some recent and earlier works. In some cases, our estimates are better than the existing coefficient bounds. Furthermore, within the engineering domain, the utilization of the Ruscheweyh derivative operator can encompass a broad spectrum of engineering applications, including the robotic manipulation control, optimizing optical systems, antenna array signal processing, image compression, and control system filter design. It emphasizes the potential for innovative solutions that can significantly enhance the reliability and effectiveness of engineering applications.

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.

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.

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.

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.

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.

A family of Analytic Functions Subordinate to Horadam Polynomials

In this paper, we introduce and investigate a family of analytic functions, denoted by $\mathcal{F}(\Pi, \alpha, \beta, \lambda, \delta, \mu)$, defined by means of Horadam polynomials. For functions in this family, 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 family.

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.

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>

Subclass of bi-starlike function associated with touchard polynomials

The current paper aims to study bi- starlike functions. It presents a new class using Touchard polynomial, which fulfills the subordination conditions. In addition, an estimation of the Taylor-Maclaurin coefficients |a2| and |a3| was found.

Bounding coefficients for certain subclasses of bi-univalent functions related to Lucas-Balancing polynomials

<abstract><p>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.</p></abstract>

Coefficient bounds for certain families of bi-Bazilevič and bi-Ozaki-close-to-convex functions

<abstract><p>The aim of this work is to introduce two families, $ \mathcal{B}_{\Sigma}(\wp; \vartheta) $ and $ \mathcal{O}_{\Sigma}(\varkappa; \vartheta) $, of holomorphic and bi-univalent functions involving the Bazilevič functions and the Ozaki-close-to-convex functions, by using generalized telephone numbers. We determinate upper bounds on the Fekete-Szegö type inequalities and the initial Taylor-Maclaurin coefficients for functions in these families. We also highlight certain edge cases and implications for our findings.</p></abstract>