Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 16 of 16
Full-Text Articles in Physical Sciences and Mathematics
On A New Subclass Of Biunivalent Functions Associated With The $(P,Q)$-Lucas Polynomials And Bi-Bazilevic Type Functions Of Order $\Rho+I\Xi$, Hali̇t Orhan, İbrahi̇m Aktaş, Hava Arikan
On A New Subclass Of Biunivalent Functions Associated With The $(P,Q)$-Lucas Polynomials And Bi-Bazilevic Type Functions Of Order $\Rho+I\Xi$, Hali̇t Orhan, İbrahi̇m Aktaş, Hava Arikan
Turkish Journal of Mathematics
Using $ (p, q) $-Lucas polynomials and bi-Bazilevic type functions of order $\rho +i\xi,$ we defined a new subclass of biunivalent functions. We obtained coefficient inequalities for functions belonging to the new subclass. In addition to these results, the upper bound for the Fekete-Szegö functional was obtained. Finally, for some special values of parameters, several corollaries were presented.
Faber Polynomial Coefficients For Certain Subclasses Of Analytic And Biunivalent Functions, Abdel Moneim Lashin, Fatma Elemam
Faber Polynomial Coefficients For Certain Subclasses Of Analytic And Biunivalent Functions, Abdel Moneim Lashin, Fatma Elemam
Turkish Journal of Mathematics
In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions defined in the open unit disc. We use the Faber polynomial expansions to find upper bounds for the $n$th$~(n\geq 3)$ Taylor-Maclaurin coefficients $\left\vert a_{n}\right\vert $ of functions belong to these new subclasses with $a_{k}=0$ for $2\leq k\leq n-1$, also we find non-sharp estimates on the first two coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $. The results, which are presented in this paper, would generalize those in related earlier works of several authors.
Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc, Sarbeswar Barik
Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc, Sarbeswar Barik
Turkish Journal of Mathematics
In this paper, we introduce two new subclasses of biunivalent functions analytic in the exterior of the unit disc. The bounds obtained for the $zero^{th}$, first and second coefficient improves upon earlier known results. The results are obtained by refining the well-known estimates for the initial coefficients of the Carth$\acute{e}$odory functions.
General Coefficient Estimates For Bi-Univalent Functions: A New Approach, Oqlah Alrefai, Mohammed Ali
General Coefficient Estimates For Bi-Univalent Functions: A New Approach, Oqlah Alrefai, Mohammed Ali
Turkish Journal of Mathematics
We prove for univalent functions $f(z)=z+\sum_{k=n}^{\infty}a_k z^k;(n\geq 2)$ in the unit disk $\mathbb{U}=\{z:\; z
On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series, Bi̇lal Şeker, Sevtap Sümer Eker
On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series, Bi̇lal Şeker, Sevtap Sümer Eker
Turkish Journal of Mathematics
In this article, we introduced a new power series whose coefficients are probabilities of the Pascal distribution. We investigated new approaches between the Pascal distribution series and some subclasses of normalized analytic functions. Also, we defined some mappings containing these functions the Alexander type integral operator. Moreover, we obtained sufficient conditions such that these mappings belong to some subclass of univalent functions.
Star-Likeness Associated With The Exponential Function, Adiba Naz, Sumit Nagpal, V. Ravichandran
Star-Likeness Associated With The Exponential Function, Adiba Naz, Sumit Nagpal, V. Ravichandran
Turkish Journal of Mathematics
Given a domain $\Omega$ in the complex plane $\mathbb{C}$ and a univalent function $q$ defined in an open unit disk $\mathbb{D}$ with nice boundary behaviour, Miller and Mocanu studied the class of admissible functions $\Psi(\Omega,q)$ so that the differential subordination $\psi(p(z),zp'(z),z^2p''(z);z)\prec h(z)$ implies $p(z)\prec q(z)$, where $p$ is an analytic function in $\mathbb{D}$ with $p(0)=1$, $\psi:\mathbb{C}^3\times \mathbb{D}\to\mathbb{C}$ and $\Omega=h(\mathbb{D})$. This paper investigates the properties of this class for $q(z)=e^z$. As application, several sufficient conditions for normalized analytic functions $f$ to be in the subclass of star-like functions associated with the exponential function are obtained.
Some Properties For A Class Of Analytic Functions Defined By A Higher-Order Differential Inequality, Oqlah Alrefai
Some Properties For A Class Of Analytic Functions Defined By A Higher-Order Differential Inequality, Oqlah Alrefai
Turkish Journal of Mathematics
Let $\mathcal{B}_p(\alpha,\beta, \lambda;j)$ be the class consisting of functions $f(z)= z^p+\sum_{k=p+1}^{\infty}a_k z^{k},\; p\in \mathbb{N}$ which satisfy $ \mathrm{Re}\left\{\alpha\frac{f^{(j)}(z)}{z^{p-j}}+\beta\frac{f^{(j+1)}(z)}{z^{p-j-1}}+\left(\frac{\beta-\alpha}{2}\right)\frac{f^{(j+2)}(z)}{z^{p-j-2}}\right\}>\lambda,\;\;(z\in \mathbb{U}=\{z:\; z (5-12\ln 2)/(44-48\ln 2)\approx -0.309$ is sufficient condition for any normalized analytic function $f$ to be starlike in $\mathbb{U}$. The results improve and include a number of known results as their special cases.
Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial, Fethi̇ye Müge Sakar, Adnan Canbulat
Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial, Fethi̇ye Müge Sakar, Adnan Canbulat
Turkish Journal of Mathematics
In this work, considering a new subclass of bi-univalent functions which are m-fold symmetric and analytic functions in the open unit disk, we determine estimates for the general Taylor-Maclaurin coefficient of the functions in this class. Furthermore, initial upper bounds of coefficients for m-fold symmetric, analytic and bi-univalent functions were found in this study. For this purpose, we used the Faber polynomial expansions. In certain cases, the coefficient bounds presented in this paper would generalize and improve some recent works in the literature. We hope that this paper will inspire future researchers in applying our approach to other related problems.
A New General Subclass Of Analytic Bi-Univalent Functions, Serap Bulut
A New General Subclass Of Analytic Bi-Univalent Functions, Serap Bulut
Turkish Journal of Mathematics
In a very recent work, Şeker [Seker B. On a new subclass of bi-univalent functions defined by using Salagean operator. Turkish Journal of Mathematics 2018; 42: 2891-2896] defined two subclasses of analytic bi-univalent functions by means of Salagean differential operator and he obtained the initial Taylor-Maclaurin coefficient estimates for functions belonging to these classes. The main purpose of this paper is to improve the results obtained by Şeker in the aforementioned study. For this purpose, we define a general subclass of bi-univalent functions.
Sandwich Theorems For A Class Of $P$-Valent Meromorphic Functionsinvolving The Erdélyi-Kober-Type Integral Operators, Hari Srivastava, Rabha Elashwah, W Kota
Sandwich Theorems For A Class Of $P$-Valent Meromorphic Functionsinvolving The Erdélyi-Kober-Type Integral Operators, Hari Srivastava, Rabha Elashwah, W Kota
Turkish Journal of Mathematics
In this paper, the authors study some subordination and superordination properties for classes of $p$-valent meromorphic, analytic, and univalent functions associated with a linear operator $\mathfrak{L}_{p,\lambda}^{m,\ell}(a,c,\mu)$ of the Erdélyi-Kober type. Connections with several earlier results are also pointed out.
On A New Subclass Of Bi-Univalent Functions Defined By Using Salagean Operator, Bi̇lal Şeker
On A New Subclass Of Bi-Univalent Functions Defined By Using Salagean Operator, Bi̇lal Şeker
Turkish Journal of Mathematics
In this manuscript, by using the Salagean operator, new subclasses of bi-univalent functions in the open unit disk are defined. Moreover, for functions belonging to these new subclasses, upper bounds for the second and third coefficients are found.
P-Subordination Chains And P-Valence Integral Operators, Erhan Deni̇z, Hali̇t Orhan, Murat Çağlar
P-Subordination Chains And P-Valence Integral Operators, Erhan Deni̇z, Hali̇t Orhan, Murat Çağlar
Turkish Journal of Mathematics
In the present investigation we obtain some sufficient conditions for the analyticity and the $p$-valence of an integral operator in the unit disk $\mathbb{D}$. Using these conditions we give some applications for a few different integral operators. The significant relationships and relevance to other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results.
Koebe Sets For The Class Of Functions Convex In Two Directions, Leopold Koczan, Pawel Zaprawa
Koebe Sets For The Class Of Functions Convex In Two Directions, Leopold Koczan, Pawel Zaprawa
Turkish Journal of Mathematics
In this paper, we consider a class $K_\alpha$ of all functions $f$ univalent in the unit disk $\Delta$ that are normalized by $f(0)=f'(0)-1=0$ while the sets $f(\Delta)$ are convex in two symmetric directions: $e^{i\alpha\pi/2}$ and $e^{-i\alpha\pi/2}$, $\alpha\in[0,1]$. It means that the intersection of $f(\Delta)$ with each straight line having the direction $e^{i\alpha\pi/2}$ or $e^{-i\alpha\pi/2}$ is either a compact set or an empty set. We find the Koebe set for $K_\alpha$. Moreover, we perform the same operation for functions in $K_{\beta, \gamma}$, i.e. for functions that are convex in two fixed directions: $e^{i\beta\pi/2}$ and $e^{i\gamma\pi/2}$, $-1\leq \beta\leq\gamma \leq 1$.
Second Hankel Determinant For Certain Subclasses Ofbi-Univalent Functions, Murat Çağlar, Erhan Deni̇z, Hari Mohan Srivastava
Second Hankel Determinant For Certain Subclasses Ofbi-Univalent Functions, Murat Çağlar, Erhan Deni̇z, Hari Mohan Srivastava
Turkish Journal of Mathematics
In the present paper, we obtain the upper bounds for the second Hankel determinant for certain subclasses of analytic and bi-univalent functions. Moreover, several interesting applications of the results presented here are also discussed.
Coefficient Estimates For General Subclasses Of $M$-Foldsymmetric Analytic Bi-Univalent Functions, Serap Bulut
Coefficient Estimates For General Subclasses Of $M$-Foldsymmetric Analytic Bi-Univalent Functions, Serap Bulut
Turkish Journal of Mathematics
In this work, we introduce and investigate two new subclasses of the bi-univalent functions in which both $f$ and $f^{-1}$ are $ m$-fold symmetric analytic functions. For functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for $ \left\vert a_{m+1}\right\vert $ and $\left\vert a_{2m+1}\right\vert .$
Coefficient Bounds For Subclasses Of M-Fold Symmetric Bi-Univalent Functions, Sevtap Sümer Eker
Coefficient Bounds For Subclasses Of M-Fold Symmetric Bi-Univalent Functions, Sevtap Sümer Eker
Turkish Journal of Mathematics
In this study, we introduce and investigate two new subclasses of the bi-univalent functions; both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric analytic functions. Among other results, upper bounds for the coefficients $\left a_{m+1}\right $ and $\left a_{2m+1}\right $ are found in this investigation.