Sibel Yalçin

Sibel Yalçin
Bursa Uludag University · Department of Mathematics

Professor

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216
Publications
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1,920
Citations

Publications

Publications (216)
Article
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We introduce a new subclass of starlike functions, denoted by , that are influenced by the Janowski functions, which are well-known in the literature. Our main results are the coefficient estimates of the inverse function and the Fekete-Szegö inequality for this subclass. We also present some special cases of our results that are of interest.
Article
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This paper establishes new results related to geometric function theory by presenting a new subclass of harmonic functions with complex values within the open unit disk, characterized by a second-order differential inequality. The investigation explores the bounds on the coefficients and estimates of the function growth. This paper also demonstrate...
Article
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In this paper, a new subclass, SC µ,p,q σ (r, s; x), of Sakaguchi-type analytic bi-univalent functions defined by (p, q)-derivative operator using Horadam polynomials is constructed and investigated. The initial coefficient bounds for |a 2 | and |a 3 | are obtained. Fekete-Szegö inequalities for the class are found. Finally, we give some corollarie...
Article
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In this article, we introduce and investigate a novel class of analytic functions that are defined through a second-order differential inequality in conjunction with the error function, a fundamental mathematical function widely used in various scientific and engineering applications. The proposed class of functions provides a versatile framework f...
Article
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The purpose of the present paper is to introduce a Wright distribution and obtain some sufficient conditions for analytic functions, whose coefficients are probabilities of the Wright distribution series, to belong to class of spiral-like univalent functions. Further, we discuss the geometric properties of an integral operator related to the Wright...
Article
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This paper introduces two novel subclasses of the function class Σ for bi-univalent functions, leveraging generalized telephone numbers and Binomial series through convolution. The exploration is conducted within the domain of the open unit disk. We delve into the analysis of initial Taylor-Maclaurin coefficients |a2| and |a3|, deriving insights an...
Article
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The Theory of Complex Functions has been studied by many scientists and its application area has become a very wide subject. Harmonic functions play a crucial role in various fields of mathematics, physics, engineering, and other scientific disciplines. Of course, the main reason for maintaining this popularity is that it has an interdisciplinary f...
Article
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In this paper, we use the linear operator Zxτ,σ(u,v,y)f(z) and the concept of the subordination to analyse the general class of all analytic univalent functions. Our main results are implication properties between the classes of such functions and the application of these properties to special cases.
Article
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In this paper, various features of a new class of normalized multivalent harmonic functions in the open unit disk are analyzed, including bounds on coefficients, growth estimations, starlikeness and convexity radii. It is further demonstrated that this class is closed when its members are convoluted. It can also be seen that various previously intr...
Article
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Recently, the (p,q)-derivative operator has been used to investigate several subclasses of analytic functions in different ways with different perspectives by many researchers. The (p,q)-derivative operator are also used to construct some subclasses of analytic functions. In this article, we investigate the (p,q)-Poisson distribution series for the...
Article
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We define two new subclasses, $\mathcal{S}_{q}^{\ast }(\alpha )$ and $\mathcal{TS}_{q}^{\ast }(\alpha )$, of analytic univalent functions. We obtain a sufficient condition for analytic univalent functions to be in $\mathcal{S}_{q}^{\ast }(\alpha )$ and we prove that this condition is also necessary for the functions in the class $\mathcal{TS}_{q}^{...
Article
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The primary motivation of the paper is to give necessary and sufficient condition for the power series distribution (Pascal model) to be in the subclasses VS p (ϑ, γ, κ) and VC p (ϑ, γ, κ) of analytic functions. Further, to obtain certain connections between the Pascal distribution series and subclasses of normalized analytic functions whose coeffi...
Article
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We preface and examine classes of (p, q)-convex harmonic locally univalent functions associated with subordination. We acquired a coefficient characterization of (p, q)-convex harmonic univalent functions. We give necessary and sufficient convolution terms for the functions we will introduce.
Article
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In this paper, we aim to find sufficient conditions for the close-to-convexity of q-Bessel–Wright functions with respect to starlike functions, such as z1−z,z1−z2, and −log(1−z) are in the open unit disc. Some consequences related to our main results are also included.
Article
We study a subclass of bi-starlike functions and obtain, for the first time, the initial seven Taylor– Maclaurin coefficient estimates |a2|, |a3|, . . . , |a7| for functions from a subclass of the function class Σ. Some new or known consequences of the accumulated results are also pointed out.
Article
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In the present paper, a new subclass of complex-valued harmonic functions in the open unit disk is introduced and coefficient bounds, growth estimates, radius of univalency, radius of starlikeness and radius of convexity of this class are investigated. In addition, it is shown that this class is closed under convolution of its members.
Article
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In this existing paper, it is aimed to set up bonds among diverse subclasses of harmonic univalent functions by implementing specific convolution operator including Pascal Distribution Series. To be more accurate, we research this kind of relations with Goodman-Rønning type harmonic univalent functions in the open unit disc.
Conference Paper
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Recently, the (p,q)-derivative operator has been used to investigate several subclasses of analytic functions in different ways with different perspectives by many researchers. The (p,q)-derivative operator are also used to construct some subclasses of analytic functions. In this article, we investigate the (p,q)-Poisson distribution series for the...
Article
Full-text available
We introduce and investigate q-analogue of a new subclass of Salagean-type harmonic univalent functions defined by subordination. We first obtained a coefficient characterization of these functions. We give necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for this subclass of harmonic univalent func...
Article
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In this paper, we introduce universally prestarlikegeneralized functions of order $\vartheta $ with $\vartheta \leq 1$ associated with shell like domain, and we getcoefficient bounds and the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ forsuch functions.
Article
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The main goal of the paper is to initiate and explore two sets of regular and bi-univalent (or bi-Schlicht) functions in 𝔇 = {𝑧 ∈ C : |𝑧| < 1} linked with Gegenbauer polynomials. We investigate certain coefficient bounds for functions in these families. Continuing the study on the initial coefficients of these families, we obtain the functional of...
Article
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In the present paper, we introduce new applications on fourth-order differential subordination associated with differential linear operator I s,r,1 (n, λ) in the punctured open unit disk U *. Also, we obtain some new results.
Article
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Lately, the q-derivative operator has been used to investigate several subclasses of harmonic functions in different ways with different perspectives by many researchers and many interesting results were obtained. The q-derivative operator are also used to construct some subclasses of harmonic functions. In this paper, we define involving of q-Pois...
Article
In the present article, a subclass of bi-starlike functions is studied and initial seven Taylor – Maclaurin coefficient estimates | a2| , | a3| , . . . , | a7| for functions in the subclass of the function class \Sigma are obtained for the first time in the literature. Few new or known consequences of the results are also pointed out.
Article
The third order differential sandwich results are obtained for multivalent analytic functions in the open unit disk by using certain classes of admissible functions. Also differential subordination and superordination results are obtained.
Conference Paper
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Harmonic functions are a classic title in the class of geometric functions. Many researchers have studied these function classes from past to present, and since it has a wide range of applications, it is still a popular class. In this study, we will examine harmonic multivalent functions, a subclass of harmonic functions. In general, harmonic multi...
Conference Paper
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Harmonic functions are a classic title in the class of geometric functions. Many researchers have studied these function classes from past to present, and since it has a wide range of applications, it is still a popular class. In this study, we will examine harmonic univalent functions, a subclass of harmonic functions. In general, harmonic univale...
Conference Paper
In this paper, we established connections between some subclasses of harmonic univalent functions by applying Hadamard product involving the Pascal distribution series.
Conference Paper
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The aim of the present study is to find the essential properties for some subclasses of harmonic univalent functions which are related to Pascal distribution that are member of the subclasses of convex univalent functions.
Article
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In this paper, we establish some results concerning the convolutions of harmonic mappings convex in the horizontal direction with harmonic vertical strip mappings. Furthermore, we provide examples illustrated graphically with the help of Maple to illuminate the results. 1. Introduction For real-valued harmonic functions and in the open unit disk t...
Article
Recently, Kumar, et al. proposed a conjecture concerning the convolution of a generalized right half-plane mapping with a vertical strip mapping. They verified this conjecture for n = 1, 2, 3 and 4. Moreover, it was proved only for β = 𝜋/2. By using of a new method, we settle this conjecture in the affirmative way for all n 𝜖 ℕ and β 𝜖 (0, 𝜋). More...
Article
In this paper, we study third-order differential subordination of univalent functions defined by differential operator. We obtain new results for thirdorder differential subordination in the open unit disk.
Article
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We introduce and investigate classes of (p,q)-starlike harmonic univalent functions defined by subordination. We first obtained a coefficient characterization of these functions. We give necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for the (p,q)-starlike harmonic univalent with negative coeffici...
Article
The aim of the current paper is to obtain the sufficient conditions and inclusion relations for Pascal distribution series to be in some subclasses of Spiral-like functions in the open unit disk U. Further, we study an integral operator related to Pascal distribution series, and some consequences and corollaries of the main results are also conside...
Preprint
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In this paper, we introduce a new subclass of harmonic functions $f=s+\overline{t}$ in the open unit disk $U =\left \{ z\in C:\left \vert z\right \vert <1\right \} $ satisfying ${\text{Re}}\left[ \gamma s^{\prime }(z)+\delta zs^{\prime \prime }(z)+\left( \frac{\delta -\gamma }{2}\right) z^{2}s^{\prime \prime \prime }\left( z\right) -\lambda \right]...
Article
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The object of the present paper is to derive some properties of holomorphic functions in the open unit disc which are defined by using a new generalized integral operator by applying a lemma due to Miller and Mocanu. Also we mention some interesting consequences of our main results.
Article
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Recently, Kumar et al. proposed a conjecture concerning the convolution of a generalized right half-plane mapping with a vertical strip mapping. They have verified the above conjecture for n=1,2,3 and 4 . Also, it has been proved only for \beta=\pi/2 . In this paper, by using of a new method, we settle this conjecture in the affirmative for all n\i...
Article
The motivation of this paper is to introduce and study a new class of univalent functions equipped with conic type regions. We also investigate a number of useful properties of this class and coefficient estimates for functions. Several consequences of the results are also pointed out.
Article
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In this paper, we find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes Wδ(α, γ, β) of analytic functions. Further, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.
Article
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In the current paper, by making use of the Horadam polynomials, we introduce and investigate a new family of holomorphic and biuniva-lent functions with respect to symmetric conjugate points defined in the open unit disk D. We derive upper bounds for the second and third coefficients and solve Fekete-Szegö problem of functions belongs to this famil...
Article
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In this article we define a class of starlike functions with respect to symmetric points in the domain of sine function. Also, we investigate coefficients bounds and upper bounds for the third order Hankel determinant for this defined class. We also evaluate the Zalcman functional |a 2 3 − a 5 |. Specializing the parameters, we improve Zalcman func...
Article
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In the present paper, we consider two new subclasses N Σ k (µ, α, τ) and N Σ k (µ, β, τ) of Σ k consisting of analytic and k-fold symmetric bi-univalent functions defined in the open unit disc U = {z : z ∈ C and |z| < 1}. For functions belonging to the two classes introduced here, we derive their normalized forms. Furthermore, we find estimates of...
Article
In this present paper, as applications of the post-quantum calculus known as the (p,q)-calculus, we construct a new class Dp,qk(γ, ζ,Ψ ) of bi-univalent functions of complex order defined in the open unit disk. Coefficients inequalities and several special consequences of the results are obtained.
Article
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In this article, we aim to find sufficient conditions for a convolution of analytic univalent functions and the Pascal distribution series to belong to the families of uniformly starlike functions and uniformly convex functions in the open unit disk $\mathbb{U}$. We also state corollaries of our main results.
Article
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We investigate specific new subclasses of the function class Σ of bi-univalent function defined in the open unit disc, which is connected with quasi-subordination. We find estimates on the Taylor-Maclaurin coefficients |a 2 | and |a 3 | for functions in these subclasses. Already pointed out are some documented and new implications of those findings...
Preprint
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In this article, we find some sufficient conditions under which the modified Lommel function is close-to-convex with respect to − log(1 − z) and 1 2 log 1+z 1−z. Starlikeness, convexity and uniformly close-to-convexity of the modified Lommel function are also discussed. Some results related to the H. Silverman are also the part of our investigation...
Conference Paper
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We have introduced a generalized class of complex-valued multivalent harmonic convex functions defined by subordination. We study some properties of our class. The results obtained here include a number of known and new results as their special cases.
Conference Paper
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In the present paper, we consider a generalized distribution with the Pascal model defined by 𝑃(𝒳 = 𝑗), 𝑗 ∈ {0,1,2,3, … } for the analytic function classes 𝐷(𝜆, 𝛼) and 𝑆∗𝐶(𝛼, 𝛿; 𝜆). Furthermore, we derive some conditions for functions in these classes.
Article
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Utilizing the concepts of subordination we have introduced a generalized class Salagean-Type of complex-valued mul-tivalent harmonic functions. We construct some properties of our class. The results obtained here include a number of known and new results as their special cases.
Article
Utilizing the concepts of subordination we have introduced a generalized class Salagean-Type of complex-valued multivalent harmonic functions. We construct some properties of our class. The results obtained here include a number of known and new results as their special cases.
Article
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The study of operators plays an essential role in Mathematics, especially in Geometric Function Theory in Complex Analysis and its related fields. Many derivative and integral operators can be written in terms of convolution of certain analytic functions. The class of analytic functions, which has an essential place in the theory of geometric funct...
Article
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In this investigation a new subclass of bi-univalent functions is established that is defined in the open unit disk Δ={𐌶 ∈ ℂ: |𐌶| < 1} and are endowed with the Sălăgean type q-difference operator. Then, Hankel inequalities for the new function class are obtained and several related consequences of the results are also stated.
Article
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In the present paper, the authors introduce some new subclasses of analytic functions in the open unit disc and investigate their inclusion relationships and convolution properties.
Article
In this present investigation, we are concerned with the class Ω m,k Σ;µ,b C 0 (α) of bi-concave functions defined by using the generalized Srivastava-Attiya operator. Moreover, we derive some coefficient inequalities for functions in this class. 2010 Mathematics Subject Classification: 30C45
Conference Paper
In this paper, we investigate certain subclasses of analytic functions defined by generalized differential operators involving binomial series. Also, we obtain coefficient estimates involving of the nonhomogeneous Cauchy-Euler differential equation of order r.
Article
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The main object of the present paper is to use the second kind Chebyshev polynomial expansions to derive estimates on the initial coefficients for a certain family of analytic and bi-univalent functions with respect to symmetric conjugate points defined in the open unit disk. Also, we solve Fekete-Szeg̈ problem for functions in this family. Further...
Article
We have constructed a subclass of analytic bi-univalent functions using (\({{\mathfrak {p}}}\),\({{\mathfrak {q}}}\))-Lucas polynomials in this research contribution. Bounds for certain coefficients and Fekete–Szegö inequalities have been estimated.
Article
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The main purpose of current paper is to obtain some new criteria for meromorphic strongly starlike functions of order α and strongly close-to-convexity of order α . Furthermore, the main results presented here are compared with the previous outcomes obtained in this area.
Article
We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in t...
Article
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In the acquaint article, we scrutinize some fundamental attribute of a subclass of harmonic univalent functions de ned by a new alteration. Like these, coefficient disparities, distortion bounds, convolutions, convex combinations and extreme points.
Article
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In this investigation, by using the Tremblay fractional derivative operator, we introduce the new class I µ,ρ Σ,γ p of bi-univalent functions based on the rule of subordination. Moreover, we use the Faber polynomial expansions and Fibonacci numbers to derive bounds for the general coefficient |an| of the bi-univalent function class.
Article
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In this paper, we introduce new concept that is fourth-order differential subordination and superordination associated with differential linear operator 𝐼𝑝(𝑛,𝜆) in open unit disk. Also, we obtain some new results.
Article
In this current work, by using a relation of subordination, we define a new subclass of starlike harmonic functions. We get coefficient bounds, distortion theorems, extreme points, convolution and convex combinations for this class of functions. Moreover, some relevant connections of the results presented here with diverse known results are briefly...
Article
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In this article, we consider some results involving the modified Salagean operator. We give coefficient bounds for these subclasses. Moreover, we discuss necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for these subclasses of functions.
Preprint
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In the present paper, we investigate connections between various subclasses of harmonic univalent functions by using a convolution operator involving the Pascal distribution series.
Article
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In this paper, we derive some applications of first order differential subordination and superordination results involving Frasin operator for analytic functions in the open unit disk. Also by these results, we obtain sandwich results. Our results extend corresponding previously known results.
Article
We want to remark explicitly that, by using the Ln(x) functions (essentially linked to Lucas polynomials of the second kind), our methodology builds a bridge, to our knowledge not previously well known, between the Theory of Geometric Functions and that of Special Functions, which are usually considered as very different fields. Thus, also making u...
Article
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In the present paper, by using the L p,q,n (x) functions, our methodology intertwine to yield the Theory of Geometric Functions and that of Special Functions, which are usually considered as very different fields. Thus, we aim at introducing a new class of bi-univalent functions defined through the (p, q)-Lucas polynomials. Furthermore, we derive c...
Article
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In this article, we introduced and defined a new class of harmonic functions which by use of a subordination. We find necessary and sufficient conditions, distortion bounds, radii of starlikeness and convexity, compactness and ex- treme points for above class of harmonic functions.
Article
Let 𝓐 denote the family of analytic functions f with f (0) = f ′(0) – 1 = 0, in the open unit disk Δ. We consider a class $$\begin{array}{} \displaystyle \mathcal{S}^{\ast}_{cs}(\alpha):=\left\{f\in\mathcal{A} : \left(\frac{zf'(z)}{f(z)}-1\right)\prec \frac{z}{1+\left(\alpha-1\right) z-\alpha z^2}, \,\, z\in \Delta\right\}, \end{array}$$ where 0 ≤...
Article
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In this paper, we are mainly interested to find sufficient conditions for the convolution operator Y λ,µ f (z) = zW λ,µ (z) * f (z) belonging to the classes UCV (k, α) , Sp (k, α) , S * ς and Cς .
Article
We introduce a new subclass of functions defined by multiplier differential operator and give coefficient bounds for these subclasses. Also, we obtain necessary and sufficient convolution conditions, distortion bounds and extreme points for these subclasses of functions.
Article
The primary motivation of the paper is to investigate the power series distribution (Pascal model) for the analytic function classes 𝑇𝒢(𝛼), 𝑇𝒢𝒮∗(𝛼, 𝜌) and 𝑇𝒢𝒞(𝛼, 𝜌). Furthermore, we give necessary and sufficient conditions for the Pascal distribution series belonging to these classes.
Article
By making use of the principle of subordination, we investigate a certain subclass of analytic functions. Such results as subordination and superordination are given. The related sandwich-type results are also presented.
Article
The motivation of this paper is to initiate connections between varied subclasses of univalent functions involving the Poisson distribution series.
Article
Full-text available
In the present investigation, we define two new subclasses of the function class Σ m 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 determine the estimates on the initial coefficients |a m+1 | and |a 2m+1 |. Also, we indicate certain s...
Article
In the present paper, we will define the bi-univalent function class SΣη,μp,q related to the (p, q)-Chebyshev polynomials. Then we will derive the (p, q)-Chebyshev polynomial bounds for the initial coefficients and determine Fekete–Szegö functional for f∈SΣη,μp,q.
Article
In this paper, we introduce and investigate a new subclass of the function class \(\Sigma \) of bi-univalent functions defined in the open unit disk, which are associated with the Sălăgean type q-difference operator and satisfy some subordination conditions. Furthermore, we find estimates on the Taylor–Maclaurin coefficients \(|a_{2}|\) and \(|a_{3...
Article
Full-text available
In this paper we introduce a new class L(; x) of Lambda-pseudo bi-starlike functions through the (p; q)-Lucas polynomials and determine the bounds for |a2| and |a3| where a2, a3 are the initial Taylor coecients of f 2 L(; x): Furthermore, we estimate the Fekete-Szego functional for f 2 L(; x): We pointed out several new or known consequences of our...
Article
The primary motivation of the paper is to give necessary and sufficient condition for the power series distribution (Pascal model) to be in the subclasses TS_{p}(λ,α,β) and UCT(λ,α,β) of analytic functions.
Article
Full-text available
In this article, the subclass of the previously described concave univalent functions is given as a preliminary information. Then, the problem of finding the upper limit of the coefficient relation |𝑎_3−𝜆𝑎_2^2| connected to the number of real values 𝜆∈(0,1] known as the Fekete-Szegö problem is briefly described. As a result, all the necessary condi...

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