Abbas Kareem Wanas

University of Al-Qadisiyah | UAQ · College of Science/ Department of Mathematics

In this paper, we introduce two new subclasses of regular and bi-univalent functions using Laguerre polynomials. Then, we define some upper limits for the Taylor Maclaurin coefficients. In addition, the Fekete-Szegö problem for the functions of the new subclasses. Finally, we provide some corollaries for certain values of parameters.

In this work, we use fractional integral and Mittag-Leffler function to obtain some results related to differential subordination and superordination defined by Hadamard product for univalent analytic functions defined in the open unit disk. These results are applied to obtain differential sandwich results. Our results extend corresponding previous...

In this paper, we introduce applications of fractional calculus techniques for a family of multivalent analytic functions defined by the Borel distribution on Hilbert space. We derive several interesting properties, including coefficient estimates, extreme points, and convex combinations.

In this article, we use the (M,N)-Lucas Polynomials to determinate upper bounds for the Taylor-Maclaurin coefficients $\left|a_{2}\right|$ and $\left| a_{3}\right|$ for functions belongs to a certain family of holomorphic and bi-univalent functions associating $\lambda$-pseudo-starlike functions with Sakaguchi type functions defined in the open uni...

In this paper, we define two families [Formula: see text] and [Formula: see text] of bi-Bazilevič and bi-Ozaki-close-to-convex functions associated with Lucas-balancing polynomials. We demonstrate the upper bounds for the initial Taylor–Maclaurin coefficients. In addition, the Fekete–Szegö type inequalities are derived for functions in these famili...

The purpose of this paper is to consider a linear operator and define a certain class of analytic and multivalent functions in the open unit disk associated with differential subordination. Also, we discuss some geometric properties for this class.

This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey’s fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional...

Let f be an analytic and normalized function in the unit disk D := {z : |z| < 1}, such that the quantity zf /f or 1 + zf /f respectively lies in a domain bounded by the Booth Lemniscate 4(1 − γ) 2 (1 − α) 2 (u − 1) 2 + 4(1 − γ) 2 (1 + α) 2 v 2 =`(u − 1) 2 + v 2´2 , where 0 < α < 1 and 0 ≤ γ < 1. We present some results on the function treatment of...

In this article, by making use of the λ-pseudo-starlike functions , we introduce a certain family of normalized analytic functions in the open unit disk U and we establish coefficient estimates for the first four determinants of the Toeplitz matrices T 2 (2), T 2 (3), T 3 (2) and T 3 (1) for the functions belonging to this family. Further, some kno...

In the present paper, we define and study a new family of holomorphic functions which involve the Bazilevič functions and the λ-pseudo-starlike functions. We establish coefficient estimates for the first four determinants of the symmetric Toeplitz matrices T2(2), T2(3), T3(1) and T3(2) for the functions in this family. Further, we investigate sever...

In this paper, we introduce and study a new families $W_{\Sigma_m}(\lambda, \gamma, \delta ; \alpha), W_{\Sigma_m}^*(\lambda, \gamma, \delta ; \beta)$, $M_{\Sigma_m}(\lambda, \gamma, \delta ; \alpha)$ and $M_{\Sigma_m}^*(\lambda, \gamma, \delta ; \beta)$ of holomorphic and $m$-fold symmetric bi-univalent functions associating the Bazilevic function...

The paper mainly investigates the initial coefficients for the subclasses of starlike functions defined by using the Cosine function involving $\alpha$ ($0\leq\alpha<1$), we obtain upper bounds for initial order of Hankel determinants and symmetric Toeplitz determinants whose elements are the initial coefficients. Also, we obtain initial coefficien...

This paper aims to study and analyze the effect of the flow rate and amplitude of walling waves on the peristaltic flow of Jeffrey’s fluid through an irregular channel. In addition, it analyses streamlined patterns and their local and global bifurcation flow. The theory of dynamical systems is used to explore the position of critical points and the...

تمت مناقشة الفئة للدوال ثنائية أحادية التكافؤ من قبل الباحث لوين وحصل على تقدير للمعامل الثاني فيها، عرَّف ساكار و واناس فئتين فرعيتين جديدتين للدوال ثنائية أحادية التكافؤ وحصلا على الحدود العليا للمعاملات الأولية |a2| و |a3| للتوابع في هذه الفئات الفرعية، دزيوك وآخرون .قدموا الفئة من الدوال الشبيهة بالصدفة المحدبة ، والتي تشير إلى وجود اتصال بين ا...

In recent years, there have been many interesting usages for differential subordinations of analytic functions in Geometric Function Theory of Complex Analysis. The concept of the first and second-order differential subordination have been pioneered by Miller and Mocanu. In 2011, the third-order differential subordination were defined to give a new...

In the present article, we introduce two families and of holomorphic and bi-univalent functions associating -pseudo-starlike and convex functions with Sakaguchi type functions defined by Gegenbauer polynomials. We derive the initial Maclaurin coefficients estimates and determinate the Fekete-Szeg problem of functions in these families.

The Ruscheweyh derivative operator is used in this paper to introduce and investigate interesting general subclasses of the function class $\Sigma_{m}$ of $m$-fold symmetric bi-univalent analytic functions. Estimates of the initial Taylor-Maclaurin coefficients $\left|a_{m+1}\right|$ and $\left|a_{2 m+1}\right|$ are obtained for functions of the su...

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-Macl...

In this work, we define and study some families of multivalent analytic functions defined by the fuzzy subordination and Borel distribution. We discuss some interesting inclusion results and various other useful properties involving integral of these families.

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 i...

In this paper, we present and investigate the notion of third-order strong differential subordinations, unveiling several intriguing properties within the context of specific classes of admissible functions. Furthermore, we extend certain definitions, presenting novel and fascinating results. We also derive several interesting properties of the res...

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...

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...

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 t...

Our paper introduces a new linear operator using the convolution between a Mittag–Leffler Function and basic hypergeometric function. Use of the linear operator creates a new class of meromorphic functions defined in the punctured open unit disk. Consequently, the paper examines different aspects Apps and assets like, extreme points, coefficient in...

In the current article, by making use of differential subordination we define and study a certain family for holomorphic functions associated with Ruscheweyh derivative operator and Borel distribution series. Also we obtain some interesting geometric properties for functions belongs to this family.

In this study, we introduce and investigate a novel subclass of analytic bi-univalent functions, which we define using Gegenbauer polynomials. We derive the initial * Corresponding Author. coefficient bounds for |a2|, |a3|, and |a4|, and establish Fekete-Szegö inequalities for this class. In addition, we confirm that Brannan and Clunie's conjecture...

The objective of this research is to produce robust differential subordination and differential superordination results using the fractional integral of the Wanas differential operator. These results apply to Analytic functions defined on , with Coefficient functions that are holomorphic in Furthermore, for each instance of strong differential subo...

The objective of this research is to produce robust differential subordination and differential superordination results using the fractional integral of the Wanas differential operator. These results apply to Analytic functions defined on , with Coefficient functions that are holomorphic in Furthermore, for each instance of strong differential subo...

In the study of geometric function theory, Legendre polynomials and other uncommon polynomials have recently gained increased importance. Using these polyno-mials, subordination, and the Al-Oboudi differential operator, we create a new class of bi-univalent functions and obtain coefficient estimates and Fekete-Szegö inequalities for this new class.

In this paper, we introduce and investigate a new family, denoted by W sc Σ (λ, η, δ, r), of normalized holomorphic and bi-univalent functions with respect to symmetric conjugate points, defined in U, by making use the Borel distribution series, which is associated with the Ho-radam polynomials. We derive estimates on the initial Taylor-Maclaurin c...

In this article, we introduce and investigate a new family of analytic and bi-prestarlike functions by using the Horadam polynomials defined in the open unit disk U. We determine upper bounds for the first two coefficients |a 2 | and |a 3 | and solve Fekete-Szegő problem of functions that belong to this family. Also, we point out several certain sp...

These authors contributed equally to this work. Abstract: The purpose of this article is to introduce and study certain families of normalized certain functions with symmetric points connected to Gegenbauer polynomials. Moreover, we determine the upper bounds for the initial Taylor-Maclaurin coefficients |a 2 | and |a 3 | and resolve the Fekete-Sze...

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 a...

The objective of this paper is to introduce and investigate two families of analytical and bi-univalent functions, and , with respect to symmetric conjugate points that are defined in the open unit disk and connected to a series of beta-negative binomial distributions. For functions in each of these families, we look into upper bounds for the initi...

The purpose of this paper is to use the second kind Chebyshev polynomials to introduce a new class of analytic and bi-univalent functions associating bi-starlike and biconvex λ-pseudo functions with Sakaguchi type functions defined in the open unit disk. We determinate upper bounds for the initial Taylor-Maclaurin coefficients |a 2 | and |a 3 | for...

Let $ \mathcal{H} $ be the family of analytic functions defined in an open unit disk $ \mathbb{U = }\left \{ z:|z| < 1\right \} $ and \begin{document}$ \mathcal{A} = \left \{ f\in \mathcal{H}:f(0) = f^{^{\prime}}(0)-1 = 0, { \ \ \ \ \ }(z\in \mathbb{U})\right \} . $\end{document} For $ A\in \mathbb{C}, B\in \lbrack-1, 0) $ and $ \gamma \in \left(\f...

One of the important problems regarding coefficients of analytical functions (i.e., Fekete–Szegö inequality) was raised by Fekete and Szegö in 1933. The results of this research are dedicated to determine upper coefficient estimates and the Fekete–Szegö problem in the class 𝒲Σ(𝛿,𝜆;𝜗), which is defined by generalized telephone numbers. We also indic...

In the current study, firstly, two new families B Σ (λ; µ) and B * Σ (λ; ν) of normalized holomorphic and bi-univalent functions are defined. Furthermore, upper bounds for the initial Taylor-Maclaurin coefficients |a 2 | and |a 3 | for functions in each of these families are acquired.

The pre-Schwarzianand Schwarzian derivatives of analytic functions f are defined in U, where U is the open unit disk. The pre-Schwarzian as well as Schwarzian derivatives are popular tools for studying the geometric properties of analytic mappings. These can also be used to obtain either necessary or sufficient conditions for the univalence of a fu...

In this article, we introduce and study the behavior of the modules of the first two coefficients for the classes NΣ(γ,λ,δ,μ;α) and NΣ*(γ,λ,δ,μ;β) of normalized holomorphic and bi-univalent functions that are connected with the prestarlike functions. We determine the upper bounds for the initial Taylor–Maclaurin coefficients |a2| and |a3| for the f...

In current manuscript, using Laguerre polynomials and (p − q)-Wanas operator, we identify upper bounds |a 2 | and |a 3 | which are first two Taylor-Maclaurin coefficients for a specific bi-univalent functions classes W Σ (η, δ, λ, σ, θ, α, β, p, q; h) and K Σ (ξ, ρ, σ, θ, α, β, p, q; h) which cover the convex and starlike functions. Also, we discus...

The object of the present work is to introduce and study a new family of analytic functions defined by Sakaguchi type functions in the open unit disk. We obtain some subordination results for this family.

In the current investigation, we study a certain family of analytic and bi-univalent functions with respect to symmetric conjugate points defined in the open unit disk U and find an upper bounds for the second Hankel determinant H 2 (2) of the functions belongs to this class.

In present paper, we use fractional integral and Wanas differential operator to obtain some subordination and superordination results associated with Hadamard product for univalent analytic functions defined in the open unit disk. These results are applied to obtain differential sandwich results. Our results extend corresponding previously known re...

The aim of the present article is to introduce and investigate a new family LΣ(δ,η,θ,t;h) of normalized holomorphic and bi-univalent functions that involve the Sakaguchi-type Bazilevič functions and Sakaguchi-type θ-pseudo-starlike functions associated with Laguerre polynomials. We obtain estimates on the initial Taylor–Maclaurin coefficients and t...

In the current work, we use the (M,N)-Lucas Polynomials to introduce a new family of holo-morphic and bi-univalent functions which involve a linear combination between Bazilevič functions and β-pseudo-starlike function defined in the unit disk D and establish upper bounds for the second and third coefficients of functions belongs to this new family...

In this work, we derive coefficient bounds for the symmetric Toeplitz matrices T2(2), T2(3), T3(1), and T3(2), which are the known first four determinants for a new family of analytic functions with Borel distribution series in the open unit disk U. Further, some special cases of results obtained are also pointed.

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.

In this current research, we introduced a new subclass of holomorphic and bi-univalent functions using q-Ruscheweyh differential operator in U. For functions in the class Σ τ,φ q (η, σ, γ), we determine estimates on the first two Taylor-Maclaurin coefficients. Also, we derive another subclass of holomorphic and bi-univalent functions as a special c...

In this article, by making use of Beta negative binomial distribution series, we introduce and study two new families O Σ (δ, η, λ, θ; µ) and O * Σ (δ, η, λ, θ; ν) of normalized holomorphic and bi-univalent functions which involve the Ozaki-close-to-convex functions. We investigate upper bounds for the initial Taylor-Maclaurin coefficients |a 2 | a...

In the present work, by making use of Gegenbauer polynomials, we introduce and study a certain family of λ -pseudo bistarlike and λ -pseudo biconvex functions with respect to symmetrical points defined in the open unit disk. We obtain estimates for initial coefficients and solve the Fekete–Szeg o ¨ problem for functions that belong to this family....

S.S. Miller and P.T. Mocanu introduced differential subordination and derived some properties associated with it. Motivated by this studies the aim of this paper is to establish some properties of differential subordination and fuzzy differential subordination associated with generalized integral operator which defined in the open unit disk.

In this work, we introduce and investigate a certain family [Formula: see text] of holomorphic and bi-univalent functions which are defined in the open unit disk [Formula: see text] associated with [Formula: see text]-Wanas operator. The estimates on the initial Taylor–Maclaurin coefficients [Formula: see text] and [Formula: see text] for the certa...

In this article, we introduce and study two new families of analytic functions by using strong differential subordinations and superordinations associated with Wanas differential operator/. We also give and establish some important properties of these families.

In this paper, we define certain families S∗E(ϑ) and CE(ϑ) of holomorphic and bi-univalent functions which are defined in the open unit disk U. We establish upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szegö type inequalities for functions in these families.

In this paper, we introduce and study a new subclass of normalized functions that are analytic and univalent in the open unit disk $ \mathbb{U} = \{z:z\in \mathcal{C}\; \; \text{and}\; \; |z| < 1\}, $ which satisfies the following geometric criterion: \begin{document}$ \begin{equation*} \Re\left(\frac{\mathcal{L}_{u, v}^{w}f(z)}{z}(1-e^{-2i\phi}\mu...

In the present paper, due to beta negative binomial distribution series and Laguerre polynomials, we investigate a new family $\mathcal{F}_{\Sigma}(\delta,\eta,\lambda,\theta;h)$ of normalized holomorphic and bi-univalent functions associated with Ozaki close-to-convex functions. We provide estimates on the initial Taylor--Maclaurin coefficients an...

In the present article, using the subordination principle, the authors employed certain generalized multiplier transform to define two new subclasses of analytic functions with respect to symmetric and conjugate points. In particular, bi-univalent conditions for function f(z) belonging to these new subclasses and their relevant connections to the f...

We introduce and study two certain classes of holomorphic and bi-univalent functions associating $\lambda$-pseudo-starlike functions with Sakaguchi-type functions. We determine upper bounds for the Taylor-Maclaurin coefficients $\vert a_2\vert$ and $\vert a_3\vert$ for functions belonging to these classes. Further we point out certain special cases...

In this paper, we determine the necessary and sufficient conditions for the power series f(z) whose coefficients are probabilities of the Borel distribution to be in the family J(p,λ ,α,β,γ) of analytic functions which defined in the open unit disk. We derive a number of important geometric properties, such as, coefficient estimates, integral repre...

In this paper, we introduce a new subclass of analytic and te-univalent functions in the open unit disc associated with the operator T λ,p,qζ , which is defined by using the (p,q)-derivative. We obtain the coefficient estimates and Fekete-Szeg˝o inequalities for the functions belonging to this class.The various results presented in this paper would...

In the current article, we introduce and investigate a new family KΣ(δ,λ,x) of analytic and bi-univalent functions by using the Horadam polynomials defined in the open unit disk U. We determine upper bounds for the initial Taylor–Maclaurin coefficients. Further we obtain the Fekete–Szegö inequality of functions belonging to this family. We also poi...

By making use of prestarlike functions, we introduce in this paper a certain family of normalized holomorphic functions defined in the open unit disk, and we establish coefficient estimates for the first four determinants of the symmetric Toeplitz matrices T2(2), T2(3), T3(2) and T3(1) for the functions belonging to this family. We also mention som...

In the present article, we introduce a new subclass of bi-close-to-convex functions in the open unit disk U defined by means of the Horadam polynomials. Estimates upper bounds for the coefficients |a 2 | and |a 3 | for functions belonging to this subclass are derived. Also, Fekete-Szegö inequalities of functions belonging to this subclass are also...

In this paper, we address the case of a particular class of function referred to as the rational equivariant functions. We investigate which elliptic zeta functions arising from integrals of power of ℘, where ℘ is the Weierstrass ℘-function attached to a rank two lattice of C, yield rational equivariant functions. Our concern in this survey is to p...

In the present paper, we determine upper bounds for the first two Taylor–Maclaurin coefficients |a2| and |a3| for a certain family of holomorphic and bi-univalent functions defined by using the Horadam polynomials. Also, we solve Fekete–Szegö problem of functions belonging to this family. Further, we point out several special cases of our results.

In the present investigation, we introduce and study a certain subclasses H Σ m (η, γ, λ , δ , τ, φ , υ; α) and H * Σ m (η, γ, λ , δ , τ, φ , υ; β) of analytic and m-fold symmetric bi-univalent functions involving φ-pseudo-starlike functions associated with Mittag-Leffler Function. We establish upper bounds for the second and third Taylor-Maclaurin...

Making use of (m, n)-Lucas polynomials, we propose a comprehensive family of regular functions of the type g(z)=z+∑j=2∞djzj which are bi-univalent in the disc {z∈C:|z|<1}. We find estimates on the coefficients |d2|, |d3| and the of Fekete–Szegö functional for members of this subfamily. Relevant connections to existing results and new consequences o...

In the present paper, making use of Gegenbauer polynomials, we initiate and explore a new family JΣ(λ,γ,s,t,q;h) of holomorphic and bi-univalent functions which were defined in the unit disk D associated with the q-Srivastava–Attiya operator. We establish the bounds for |a2| and |a3|, where a2, a3 are the initial Taylor–Maclaurin coefficients. For...

The purpose of this work is to use fractional integral and Wanas operator to define a certain class of analytic and univalent functions defined in the open unit disk U. Also, we obtain some results for this class such as integral representation, inclusion relationship and argument estimate.

In the present paper, we introduce and study a subclass of analytic and univalent functions associated with Beta negative binomial distribution series which is defined in the open unit disk U. We discuss some important geometric properties of this subclass, like, coefficient estimates, extreme points and integral representation. Also, we obtain res...

In this article, we establish the bounds for the initial Taylor–Maclaurin coefficients |a2| and |a3| for a new family GΣ(δ,ξ,λ;h) of holormorphic and bi-univalent functions which involve the prestarlike functions. Furthermore, for the family functions GΣ(δ,ξ,λ;h) we investigate the Fekete–Szegö type inequality, special cases and consequences.

In the current article, making use of certain operator, we initiate and explore a certain family WS(l, g, s, d, a, b, p, q; h) of holomorphic and bi-univalent functions in the open unit disk D. We establish upper bounds for the initial Taylor–Maclaurin coefficients and the Fekete–Szegö type inequality for functions in this family.

In the present investigation, we use the principle of subordination to introduce a new family for holomorphic functions defined by generalized differential operator. Also we establish some interesting geometric properties for functions belonging to this family.

In current effort, by making use of the principle of subordination, we introduce and study a new family of holomorphic and bi-univalent functions which are defined in open unit disk and solve Fekete-Szegö problem for functions which belong to this family.

The motivation of the present paper is to define q-analogue of Wanas operator in geometric function theory. We also introduce certain families T σ,α Σm (t, n, β, q, δ) and T σ,α Σm (t, n, β, q, γ) of holormorphic and m-fold symmetric bi-univalent functions associated with q-analogue of Wanas operator. The upper bounds for the second and third Taylo...

In the present article, we define a new family for holomorphic functions (so-called Bazilevic-Sakaguchi type functions) and determinate strong differential subordination and superordination results for these new functions by investigating certain suitable classes of admissible functions. These results are applied to obtain strong differential sandw...

The aim of this paper is to use (U, V)-Lucas polynomials to introduce and study a new family of holomorphic and bi-univalent functions defined in the open unit disk which involve q-derivative operator. We investigate upper bounds for the Taylor-Maclaurin coefficients |d 2 | and |d 3 | and Fekete-Szegö problem for functions belongs to this new famil...

Making use of Gegenbauer polynomials, we initiate and explore a comprehensive family of regular and bi-univalent (or bi-Schlicht) functions in D = {z ∈ C : |z| < 1}. We investigate certain coefficients bounds and the Fekete-Szegö functional for functions in this family. We also present few interesting observations and provide relevant connections o...

In this article, we introduce and study a new family P Σ (δ, λ, k, γ, α, β, r) of normalized analytic and λ-pseudo-starlike bi-univalent functions by using the Horadam polynomials, which is associated with a certain convolution operator defined in the open unit disk U. We establish the bounds for |a 2 | and |a 3 |, where a 2 , a 3 are the initial T...

In the present paper, we introduce and study two new subclasses of analytic and $m$-fold symmetric bi-univalent functions defined in the open unit disk $U$. Furthermore, for functions in each of the subclasses introduced here, we obtain upper bounds for the initial coefficients $\left| a_{m+1}\right|$ and $\left| a_{2m+1}\right|$. Also, we indicate...

In this current study, we introduce and investigate a new subclass of holormorphic and bi-univalent functions Eη,φ(θ) in the unit disk ⋋ associated with q-derivative operator. The coefficient estimates |b2| and |b3| on the new subclass are obtained and important results are indicated.

In this article, by making use of Horadam polynomials, we introduce and investigate a certain family TΣ(λ,α,β,k,γ;x) of analytic and bi- univalent functions associated with Wanas operator which defined in the open unit disk U. We establish upper bounds for the initial Taylor- Maclaurin coefficients and obtain the Fekete-Szeg ̈o inequality of functi...

In this paper, by making use of Borel distribution we introduce a new family G Σ (δ, γ, λ, τ, r) of normalized analytic and bi-univalent functions in the open unit disk U, which are associated with Horadam polynomials. We establish upper bounds for the initial Taylor-Maclaurin coefficients |a 2 | and |a 3 | of functions belonging to the analytic an...

In present manuscript, we introduce and study two families BΣ(λ, δ; α) and B * Σ (λ, δ; β) of holomorphic and bi-univalent functions which involve the Borel distribution series. We establish upper bounds for the initial Taylor-Maclaurin coefficients |a2| and |a3| for functions in each of these families. We also point out special cases and consequen...

In this paper, we use the (M,N)-Lucas polynomials to establish upper bounds for the second and third coefficients of functions belonging to a new family of of λ-pseudo bi-starlike and λ-pseudo bi-convex functions with respect to symmetrical points defined in the open unit disk D. Also, we discuss the Fekete-Szegö problem for functions which belong...

The motivation of the present article is to define the (p-q)-Wanas operator in geometric function theory by the symmetric nature of quantum calculus. We also initiate and explore certain new families of holormorphic and bi-univalent functions AE(l, s, d, s, t, p, q; J) and SE(m, g, s, d, s, t, p, q; J) which are defined in the unit disk U associate...

In this paper, we discuss the upper bounds for the second Hankel determinant H 2 (2) of a new subclass of λ-pseudo-starlike bi-univalent functions defined in the open unit disk U .

The aim of this article is to initiating an exploration of the properties of bi-univalent functions related to Gegenbauer polynomials. To do so, we introduce a new families \mathbb{T}_\Sigma (\gamma, \phi, \mu, \eta, \theta, \gimel, t, \delta) and \mathbb{S}_\Sigma (\sigma, \eta, \theta, \gimel, t, \delta ) of holomorphic and bi-univalent functions...

The main purpose of this paper is to find upper bounds for the second and third Taylor–Maclaurin coefficients for two families of holomorphic and bi-univalent functions associated with Wanas operator. Further, we point out certain special cases for our results.

In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family SWΣ(δ,γ,λ,s,t,q,r) of normalized holomorphic and bi-univalent functions in the open unit disk U, which are associated with the Bazilevič functions and the λ-pseudo-starlike functions as well as the Horadam polynomials. We estimate the secon...

In this article, we define two new families $\mathcal{T}_{\Sigma}(\mu,\gamma,\lambda;\alpha)$ and $\mathcal{T}_{\Sigma}^{*}(\mu,\gamma,\lambda;\beta)$ of normalized holomorphic and bi-univalent functions which involve the Bazilevi\v{c} functions and the $\lambda$-pseudo-starlike functions. For functions in each of these families, we establish the b...

In present article, we introduce and study a certain family of analytic functions defined by Wanas operator in the open unit disk. We establish some important geometric properties for this family. Further we point out certain special cases for our results.