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2020

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Articles 1141 - 1170 of 1326

Full-Text Articles in Mathematics

A New Solution To The Discontinuity Problem On Metric Spaces, Ufuk Çeli̇k, Ni̇hal Özgür Jan 2020

A New Solution To The Discontinuity Problem On Metric Spaces, Ufuk Çeli̇k, Ni̇hal Özgür

Turkish Journal of Mathematics

We study on the Rhoades' question concerning the discontinuity problem at fixed point for a self-mapping T of a metric space. We obtain a new solution to this question. Our result generalizes some recent theorems existing in the literature and implies the uniqueness of the fixed point. However, there are also cases where the fixed point set of a self-mapping contains more than 1 element. Therefore, by a geometric point of view, we extend the Rhoades' question to the case where the fixed point set is a circle. We also give a solution to this extended version.

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Analytic Functions Associated With Cardioid Domain, Sarfraz Nawaz Malik, Mohsan Raza, Janusz Sokol, Saira Zainab Jan 2020

Analytic Functions Associated With Cardioid Domain, Sarfraz Nawaz Malik, Mohsan Raza, Janusz Sokol, Saira Zainab

Turkish Journal of Mathematics

In this article, we define and study new domain for analytic functions which is named as cardioid domain for being of cardioid structure. Analytic functions producing cardioid domain are defined and studied to some extent. The Fekete-Szegö inequality is also investigated for such analytic functions.

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Gradient Weyl-Ricci Soliton, Cornelia-Livia Bejan, Şemsi̇ Eken Meri̇ç, Erol Kiliç Jan 2020

Gradient Weyl-Ricci Soliton, Cornelia-Livia Bejan, Şemsi̇ Eken Meri̇ç, Erol Kiliç

Turkish Journal of Mathematics

The classical notion of gradient Ricci soliton is extended here to the gradient Weyl-Ricci soliton. A Weyl structureofthebasemanifold M is lifted to its tangent bundle TM, by using the Sasaki metric. We give some necessary and sufficient conditions such that the Weyl structure on TM to be a gradient Weyl-Ricci soliton.

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An Extragradient Algorithm For Split Generalized Equilibrium Problem And The Set Of Fixed Points Ofquasi-$\Phi $-Nonexpansive Mappings In Banach Spaces, Olawale Oyewole, Oluwatosin Mewomo, Lateef Jolaoso, Safeer Hussain Khan Jan 2020

An Extragradient Algorithm For Split Generalized Equilibrium Problem And The Set Of Fixed Points Ofquasi-$\Phi $-Nonexpansive Mappings In Banach Spaces, Olawale Oyewole, Oluwatosin Mewomo, Lateef Jolaoso, Safeer Hussain Khan

Turkish Journal of Mathematics

In this paper, we study the problem of finding a common solution to split generalized mixed equilibrium problem and fixed point problem for quasi-$% \phi $-nonexpansive mappings in 2-uniformly convex and uniformly smooth Banach space $E_1$ and a smooth, strictly convex, and reflexive Banach space $% E_2$. An iterative algorithm with Armijo linesearch rule for solving the problem is presented and its strong convergence theorem is established. The convergence result is obtained without using the hybrid method which is mostly used when strong convergence is desired. Finally, numerical experiments are presented to demonstrate the practicability, efficiency, and performance of our …

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Max Cs And Min Cs Modules, Truong Dinh Tu, Thuat Do Jan 2020

Max Cs And Min Cs Modules, Truong Dinh Tu, Thuat Do

Turkish Journal of Mathematics

In this work, we study max CS, min CS, max-min CS modules and their endomorphism rings. Under certain conditions (e.g., related to nonsingularity and duo-ness), we prove that a module is max CS if and only if it is min CS, and that direct sums of min (max) CS modules is again min (max) CS. Finally, symmetry of max-min CS property on the endomorphism rings of max-min CS modules is investigated.

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Dual And Canonical Dual Of Controlled K-G-Frames In Hilbert Spaces, Hessam Hosseinnezhad Jan 2020

Dual And Canonical Dual Of Controlled K-G-Frames In Hilbert Spaces, Hessam Hosseinnezhad

Turkish Journal of Mathematics

This paper is devoted to studying the controlled dual K-g-Bessel sequences of controlled K-g-frames. In fact, we introduce the concept of dual K-g-Bessel sequences of controlled K-g-frames and then, we present some necessary and/or sufficient conditions under which a controlled g-Bessel sequence is a controlled dual K-g-frame of a given controlled K-g-frame. Subsequently, we pay attention to investigating the structure of the canonical controlled dual K-g-Bessel sequence of a Parseval controlled K-g-frame and some other related results.

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A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Paksoy Jan 2020

A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Paksoy

Turkish Journal of Mathematics

In this work we construct a cone comprised of a group of tensors (hypermatrices) satisfying a special condition, and we study its relations to structured tensors such as M-tensors and H-tensors. We also investigate its applications to spectra of certain Z-tensors. We obtain an inequality for the spectral radius of certain tensors when the order m is odd.

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Abstract Korovkin-Type Theorems In The Filter Setting With Respect To Relative Uniform Convergence, Antonio Boccuto, Kami̇l Demi̇rci̇, Sevda Yildiz Jan 2020

Abstract Korovkin-Type Theorems In The Filter Setting With Respect To Relative Uniform Convergence, Antonio Boccuto, Kami̇l Demi̇rci̇, Sevda Yildiz

Turkish Journal of Mathematics

We prove a Korovkin-type approximation theorem using abstract relative uniform filter convergence of a net of functions with respect to another fixed filter, a particular case of which is that of all neighborhoods of a point, belonging to the domain of the involved functions. We give some examples, in which we show that our results are strict generalizations of the classical ones.

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A Semi-Markovian Renewal Reward Process With $\Gamma(G)$ Distributed Demand, Asli Bektaş Kamişlik, Büşra Alakoç, Tülay Kesemen, Tahi̇r Khani̇yev Jan 2020

A Semi-Markovian Renewal Reward Process With $\Gamma(G)$ Distributed Demand, Asli Bektaş Kamişlik, Büşra Alakoç, Tülay Kesemen, Tahi̇r Khani̇yev

Turkish Journal of Mathematics

We consider a classical semi-Markovian stochastic model of type $(s,S)$ with Logistic distributed demand random variables. Logistic distribution is a member of special distribution class known as $\Gamma(g)$ that encounters in many real-life applications involving extreme value theory. The objective of this study is to observe some major characteristics of a stochastic process $X(t)$ which represents semi-Markovian renewal reward process of type $(s,S)$. We used new approximation results for renewal function that allow us to obtain three-term asymptotic expansion for ergodic distribution function and for $n^{th}$ order moments of ergodic distribution of the process $X(t)$.

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On A Three-Dimensional Solvable System Of Difference Equations, Yacine Halim, Massaoud Berkal, Amira Khelifa Jan 2020

On A Three-Dimensional Solvable System Of Difference Equations, Yacine Halim, Massaoud Berkal, Amira Khelifa

Turkish Journal of Mathematics

In this paper we solve the following system of difference equations \begin{equation*} x_{n+1}=\dfrac{z_{n-1}}{a+by_nz_{n-1}},\quad y_{n+1}=\dfrac{x_{n-1}}{a+bz_nx_{n-1}},\quad z_{n+1}=\dfrac{y_{n-1}}{a+bx_ny_{n-1}},\quad n\in \mathbb{N}_{0} \end{equation*} where parameters $a, b$ and initial values $x_{-1},x_{0},y_{-1},y_{0},z_{-1},z_{0}$ are nonzero real numbers, and give a representation of its general solution in terms of a specially chosen solutions to homogeneous linear difference equation with constant coefficients associated to the system.

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Solvability And Maximal Regularity Results For A Differential Equation With Diffusion Coefficient, Kordan Ospanov, Adilet Yesbayev Jan 2020

Solvability And Maximal Regularity Results For A Differential Equation With Diffusion Coefficient, Kordan Ospanov, Adilet Yesbayev

Turkish Journal of Mathematics

We consider a second-order differential equation with rapidly growing intermediate coefficients. We obtain a solvability result in the cases that the diffusion coefficient of equation is unbounded or it tends to zero at the infinity. Under additional conditions, we prove the $L_p - $ maximal regularity estimate for the solution of this equation.

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Faber Polynomial Coefficients For Certain Subclasses Of Analytic And Biunivalent Functions, Abdel Moneim Lashin, Fatma Elemam Jan 2020

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.

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On Lyapunov-Type Inequalities For Boundary Value Problems Of Fractional Caputo-Fabrizio Derivative, Şuayi̇p Toprakseven Jan 2020

On Lyapunov-Type Inequalities For Boundary Value Problems Of Fractional Caputo-Fabrizio Derivative, Şuayi̇p Toprakseven

Turkish Journal of Mathematics

In this study, Lyapunov-type inequalities for fractional boundary value problems involving the fractional Caputo Fabrizio differential equation with mixed boundary conditions when the fractional order of $\beta \in (1,2]$ and Dirichlet-type boundary condition when the fractional order of $\sigma \in (2,3]$ have been derived. Some consequences of the results related to the fractional Sturm?Liouville eigenvalue problems have also been given. Additionally, we examine the nonexistence of the solution of the fractional boundary value problem.

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Remarks On The One-Dimensional Sloshing Problem Involving The $P$-Laplacian Operator, Wei-Chuan Chen, Yanhsiou Cheng Jan 2020

Remarks On The One-Dimensional Sloshing Problem Involving The $P$-Laplacian Operator, Wei-Chuan Chen, Yanhsiou Cheng

Turkish Journal of Mathematics

In this paper, we study the inverse nodal problem and the eigenvalue gap for the one-dimensional sloshing problem with the $p$-Laplacian operator. By applying the Prüfer substitution, we first derive the reconstruction formula of the depth function by using the information of the nodal data. Furthermore, we employ the Tikhonov regularization method to consider how to reconstruct the depth function using only zeros of one eigenfunction. Finally, we investigate the eigenvalue gap under the restriction of symmetric single-well depth functions. We show the gap attains its minimum when the depth function is constant.

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On Holomorphic Poly-Norden Manifolds, Çağri Karaman, Zühre Topuz Jan 2020

On Holomorphic Poly-Norden Manifolds, Çağri Karaman, Zühre Topuz

Turkish Journal of Mathematics

In this paper, we investigated a new manifold with a poly-Norden structure, which is inspired by the positive root of the equation $x^{2}-mx-1=0$. We call this new manifold as holomorphic poly-Norden manifolds. We examine some properties of the Riemann curvature tensor and give an example of this manifold. Then, we define a different connection on this manifold which is named the semisymmetric metric poly F-connection and study some properties of the curvature and torsion tensor field according to this connection.

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Some Results On Prime Rings With Multiplicative Derivations, Gurninder Singh Sandhu, Di̇dem Karalarlioğlu Camci Jan 2020

Some Results On Prime Rings With Multiplicative Derivations, Gurninder Singh Sandhu, Di̇dem Karalarlioğlu Camci

Turkish Journal of Mathematics

Let $R$ be a prime ring with center $Z(R)$ and an automorphism $\alpha.$ A mapping $\delta:R\to R$ is called multiplicative skew derivation if $\delta(xy)=\delta(x)y+ \alpha(x)\delta(y)$ for all $x,y\in R$ and a mapping $F:R\to R$ is said to be multiplicative (generalized)-skew derivation if there exists a unique multiplicative skew derivation $\delta$ such that $F(xy)=F(x)y+\alpha(x)\delta(y)$ for all $x,y\in R.$ In this paper, our intent is to examine the commutativity of $R$ involving multiplicative (generalized)-skew derivations that satisfy the following conditions: (i) $F(x^{2})+x\delta(x)=\delta(x^{2})+xF(x)$, (ii) $F(x\circ y)=\delta(x\circ y)\pm x\circ y$, (iii) $F([x,y])=\delta([x,y])\pm [x,y]$, (iv) $F(x^{2})=\delta(x^{2})$, (v) $F([x,y])=\pm x^{k}[x,\delta(y)]x^{m}$, (vi) $F(x\circ y)=\pm x^{k}(x\circ\delta(y))x^{m}$, (vii) $F([x,y])=\pm …

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$T$-Soft Equality Relation, Tareq Alshami, Mohammed El-Shafei Jan 2020

$T$-Soft Equality Relation, Tareq Alshami, Mohammed El-Shafei

Turkish Journal of Mathematics

The desire of generalizing some set-theoretic properties to the soft set theory motivated many researchers to define various types of soft operators. For example, they redefined the complement of a soft set, and soft union and intersection between two soft sets in a way that satisfies De Morgan's laws. In this paper, we introduce and study the concepts of $T$-soft subset and $T$-soft equality relations. Then, we utilize them to define the concepts of $T$-soft union and $T$-soft intersection for arbitrary family of soft sets. By $T$-soft union, we successfully keep some classical properties via soft set theory. We conclude …

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On The Variational Curves Due To The Ed-Frame Field In Euclidean 4-Space, Muradi̇ye Çi̇mdi̇ker, Yasi̇n Ünlütürk Jan 2020

On The Variational Curves Due To The Ed-Frame Field In Euclidean 4-Space, Muradi̇ye Çi̇mdi̇ker, Yasi̇n Ünlütürk

Turkish Journal of Mathematics

In this study, we define a variational field for constructing a family of Frenet curvesof the length l lying on a connected oriented hypersurface and calculate the length of the variational curves due to the ED-frame field in Euclidean 4-space. And then, we derive the intrinsic equations for the variational curves and also obtain boundary conditions for this type of curves due to the ED-frame field in Euclidean 4-space.

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Units And 2-Class Field Towers Of Some Multiquadratic Number Fields, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini, Abdelmalek Azizi Jan 2020

Units And 2-Class Field Towers Of Some Multiquadratic Number Fields, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini, Abdelmalek Azizi

Turkish Journal of Mathematics

In this paper, we investigate the unit groups, the 2-class groups, the 2-class field towers and the structures of the second 2-class groups of some multiquadratic number fields of degree 8 and 16.

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On 3-Dimensional Almost Einstein Manifolds With Circulant Structures, Iva Dokuzova Jan 2020

On 3-Dimensional Almost Einstein Manifolds With Circulant Structures, Iva Dokuzova

Turkish Journal of Mathematics

A 3-dimensional Riemannian manifold equipped with a tensor structure of type (1,1), whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e. these structures are circulant. An associated manifold, whose metric is expressed by both structures, is studied. Three classes of such manifolds are considered. Two of them are determined by special properties of the curvature tensor of the manifold. The third class is composed by manifolds whose structure is parallel with respect to the Levi-Civitaconnection of the metric. Some geometric characteristics of these manifolds are obtained. Examples …

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On Ulam's Type Stability Criteria For Fractional Integral Equations Including Hadamard Type Singular Kernel, Yasemi̇n Başci, Süleyman Öğrekçi̇, Adi̇l Misir Jan 2020

On Ulam's Type Stability Criteria For Fractional Integral Equations Including Hadamard Type Singular Kernel, Yasemi̇n Başci, Süleyman Öğrekçi̇, Adi̇l Misir

Turkish Journal of Mathematics

In this paper, we deal with the Hyers-Ulam-Rassias (HUR) and Hyers-Ulam (HU) stability of Hadamard type fractional integral equations on compact intervals. The stability conditions are developed using a new generalized metric (GM) definition and the fixed point technique by motivating Wang and Lin Ulam's type stability of Hadamard type fractional integral equations. Filomat 2014; 28(7): 1323-1331. Moreover, our approach is efficient and ease in use than to the previously studied approaches. Finally, we give two examples to explain our main results.

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Asymptotic Socle Behaviors For Cones Over Curves In Positive Characteristic, Jinjia Li Jan 2020

Asymptotic Socle Behaviors For Cones Over Curves In Positive Characteristic, Jinjia Li

Turkish Journal of Mathematics

This paper studies the distribution of socle degrees of $R/I^{[p^e]}$ when $e$ is large, for a homogeneous ideal $I$ in a two-dimensional standard-graded normal domain $R$ in positive characteristic $p$. We prove that the distribution is very much related to the asymptotic slopes of the syzygy bundle Syz$(I)$, which have been known to determine the Hilbert-Kunz multiplicity of $I$.

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The Meyer Function On The Handlebody Group, Yusuke Kuno, Masatoshi Sato Jan 2020

The Meyer Function On The Handlebody Group, Yusuke Kuno, Masatoshi Sato

Turkish Journal of Mathematics

We give an explicit formula for the signature of handlebody bundles over the circle interms of the homological monodromy. This gives a cobounding function of Meyer's signature cocycle on the mapping class group of a 3-dimensional handlebody, i.e. the handlebody group. As an application, we give a topological interpretation for the generator of the first cohomology group of the hyperelliptic handlebody group.

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On Quasi-Affinity And Reducing Subspaces Of Multiplication Operator On A Certain Closed Subspace, Yucheng Li, Lina Song, Wenhua Lan Jan 2020

On Quasi-Affinity And Reducing Subspaces Of Multiplication Operator On A Certain Closed Subspace, Yucheng Li, Lina Song, Wenhua Lan

Turkish Journal of Mathematics

Let $H$ denote a certain closed subspace of the Bergman space $A_{\alpha}^{2}({\B}_{n})(\alpha>-1)$ of the unit ball in $\mathbb{C}^{n}$. In this paper, we prove that the operator $\bigoplus\limits_{1}^{m}M_{z^{(s_{1},\cdots,s_{n})}}$ is quasi-affine to the multiplication operator $M_{z^{(ms_{1},\cdot\cdot\cdot,ms_{n})}}$ on $H$. Furthermore, the reducing subspaces of $M_{z^{(ms_{1},\cdots,ms_{n})}}$ are characterized on $H$.

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On Some Sums At The $A$-Points Of The $K$-Th Derivatives Of The Dirichlet $L$-Functions, Mohammed Mekkaoui, Abdallah Derbal, Kamel Mazhouda Jan 2020

On Some Sums At The $A$-Points Of The $K$-Th Derivatives Of The Dirichlet $L$-Functions, Mohammed Mekkaoui, Abdallah Derbal, Kamel Mazhouda

Turkish Journal of Mathematics

Let $L^{(k)}(s,\chi)$ be the $k$-th derivative of the Dirichlet L-function associated with a primitive character $\chi$ mod $q$ and $a$ be a complex number. The solutions of $L^{(k)}(s,\chi)=a$ are called $a$-points. In this paper, we give an asymptotic formula for the sums

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Characterizations Of Dual Curves And Dual Focal Curves In Dual Lorentzian Space $ D^{3}_{1} $, Sareh Mehdizadeh Gilani, Nemat Abazari, Yusuf Yayli Jan 2020

Characterizations Of Dual Curves And Dual Focal Curves In Dual Lorentzian Space $ D^{3}_{1} $, Sareh Mehdizadeh Gilani, Nemat Abazari, Yusuf Yayli

Turkish Journal of Mathematics

In this paper, we have introduced dual Lorentzian connection, bracket and curvature tensor on dual Lorentzian space $ D_{1}^{3} .$ We have studied a dual curve in different situations in dual Lorentzian space $D^{3}_{1} $ and have found Bishop Darboux vector and some relations according to this vector field, Bishop frame and focal curve of the present dual curve. It has been shown that Bishop Darboux vector has a similar amount in three different cases of a dual curve and the first dual focal curvature of the aforementioned curve is constant function.

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Linear Mappings Satisfying Some Recursive Sequences, Amin Hosseini, Mehdi Mohammadzadeh Karizaki Jan 2020

Linear Mappings Satisfying Some Recursive Sequences, Amin Hosseini, Mehdi Mohammadzadeh Karizaki

Turkish Journal of Mathematics

Let $\mathcal{A}$ be a unital, complex normed $\ast$-algebra with the identity element $\textbf{e}$ such that the set of all algebraic elements of $\mathcal{A}$ is norm dense in the set of all self-adjoint elements of $\mathcal{A}$ and let $\{D_n\}_{n = 0}^{\infty}$ and $\{\Delta_n\}_{n = 0}^{\infty}$ be sequences of continuous linear mappings on $\mathcal{A}$ satisfying \[ \left\lbrace \begin{array}{c l} D_{n + 1}(p) = \sum_{k = 0}^{n}D_{n - k}(p)D_k(p),\\ \\ \Delta_{n + 1}(p) = \sum_{k = 0}^{n}\Delta_{n - k}(p)D_k(p), \end{array} \right. \] for all projections $p$ of $\mathcal{A}$ and all nonnegative integers $n$. Moreover, suppose that $D_0(p) = D_0(p)^2$ holds for all projections …

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On Basicity Of The System Of Eigenfunctions Of One Discontinuous Spectral Problem For Second Order Differential Equation For Grand-Lebesgue Space, Yusuf Zeren, Miqdad Ismailov, Fati̇h Şi̇ri̇n Jan 2020

On Basicity Of The System Of Eigenfunctions Of One Discontinuous Spectral Problem For Second Order Differential Equation For Grand-Lebesgue Space, Yusuf Zeren, Miqdad Ismailov, Fati̇h Şi̇ri̇n

Turkish Journal of Mathematics

Basicity of the system of eigenfunctions of some\textbf{ }discontinuous spectral problem for a second order differential equation with spectral parameter in boundary condition for grand-Lebesgue space $L_{p)} (-1;1)$ is studied in this work. Since the space is nonseparable, a subspace suitable for the spectral problem is defined. The subspace $G_{p)} (-1;1)$ of $L_{p)} (-1;1)$ generated by shift operator is considered. Basicity of the system of eigenfunctions for the space $G_{p)} (-1;1)\oplus C$, $1

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On The Dynamics Of Certain Higher-Order Scalar Difference Equation: Asymptotics, Oscillation, Stability, Pavel Nesterov Jan 2020

On The Dynamics Of Certain Higher-Order Scalar Difference Equation: Asymptotics, Oscillation, Stability, Pavel Nesterov

Turkish Journal of Mathematics

We construct the asymptotics for solutions of the higher-order scalar difference equation that is equivalent to the linear delay difference equation $\Delta y(n)=-g(n)y(n-k)$. We assume that the coefficient of this equation oscillates at the certain level and the oscillation amplitude decreases as $n\to\infty$. Both the ideas of the centre manifold theory and the averaging method are used to construct the asymptotic formulae. The obtained results are applied to the oscillation and stability problems for the solutions of the considered equation.

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Various Results For Series Expansions Of The Error Functions With The Complex Variable And Some Of Their Implications, Hüseyi̇n Irmak Jan 2020

Various Results For Series Expansions Of The Error Functions With The Complex Variable And Some Of Their Implications, Hüseyi̇n Irmak

Turkish Journal of Mathematics

This scientific investigation deals with introducing certain basic information relating to the error functions in z-plane, establishing extensive relations between various series expansions of the complex error functions and presenting a number of their implications.

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