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Degree Of Approximation By Means Of Hexagonal Fourier Series, Ali̇ Güven
Degree Of Approximation By Means Of Hexagonal Fourier Series, Ali̇ Güven
Turkish Journal of Mathematics
Let $f$ be a continuous function which is periodic with respect to the hexagon lattice, and let $A$ be a lower triangular infinite matrix of nonnegative real numbers with nonincreasing rows. The degree of approximation of the function $f$ by matrix means $T_{n}^{\left( A\right) }\left( f\right) $ of its hexagonal Fourier series is estimated in terms of the modulus of continuity of $f.$
Korovkin-Type Theorems And Their Statistical Versions In Grand Lebesgue Spaces, Yusuf Zeren, Miqdad Ismailov, Cemi̇l Karaçam
Korovkin-Type Theorems And Their Statistical Versions In Grand Lebesgue Spaces, Yusuf Zeren, Miqdad Ismailov, Cemi̇l Karaçam
Turkish Journal of Mathematics
The analogs of Korovkin theorems in grand-Lebesgue spaces are proved. The subspace $G^{p)} (-\pi ;\pi )$ of grand Lebesgue space is defined using shift operator. It is shown that the space of infinitely differentiable finite functions is dense in $G^{p)}(-\pi ;\pi )$. The analogs of Korovkin theorems are proved in $G^{p)} (-\pi ;\pi )$. These results are established in $G^{p)} (-\pi ;\pi )$ in the sense of statistical convergence. The obtained results are applied to a sequence of operators generated by the Kantorovich polynomials, to Fejer and Abel-Poisson convolution operators.
The Fekete-Szegö Inequality For Subclasses Of Analytic Functions Related To Modified Sigmoid Functions, Muhammet Kamali̇, Hali̇t Orhan, Murat Çağlar
The Fekete-Szegö Inequality For Subclasses Of Analytic Functions Related To Modified Sigmoid Functions, Muhammet Kamali̇, Hali̇t Orhan, Murat Çağlar
Turkish Journal of Mathematics
In this paper, the authors investigate the initial coefficient bounds for a new generalized subclass of analytic functions related to Sigmoid functions. Also, the relevant connections with the famous classical Fekete?Szegö inequality for these classes are discussed.
The Homogenization Of Diffusion-Convection Equations In Non-Periodic Structures, Anvarbek Meirmanov, Oleg Galtsev
The Homogenization Of Diffusion-Convection Equations In Non-Periodic Structures, Anvarbek Meirmanov, Oleg Galtsev
Turkish Journal of Mathematics
We consider the homogenization of diffusion-convective problems with given divergence-free velocities in nonperiodic structures defined by sequences of characteristic functions(the first sequence). These quence of concentration (the second sequence)is uniformly bounded in the space of square-summable functions with square-summable derivatives with respect to spatial variables. At the same time, the sequence of time-derivative of product of these concentrations on the characteristic functions, that define a nonperiodic structure, is bounded in the space of square-summable functions from time interval into the conjugated space of functions depending on spatial variables, withsquare-summable derivatives. We prove the strong compactness of the second sequences in …
An Improved Trudinger--Moser Inequality And Its Extremal Functions Involving $L^P$-Norm In $\Mathbb{R}^2$, Xiaomeng Li
An Improved Trudinger--Moser Inequality And Its Extremal Functions Involving $L^P$-Norm In $\Mathbb{R}^2$, Xiaomeng Li
Turkish Journal of Mathematics
Let $W^{1,2}(\mathbb{R}^2)$ be the standard Sobolev space. Denote for any real number $p>2$ \begin{align*}\lambda_{p}=\inf\limits_{u\in W^{1,2}(\mathbb{R}^2),u\not\equiv0}\frac{\int_{\mathbb{R}^{2}}( \nabla u ^2+ u ^2)dx}{(\int_{\mathbb{R}^{2}} u ^pdx)^{2/p}}. \end{align*} Define a norm in $W^{1,2}(\mathbb{R}^2)$ by \begin{align*}\ u\ _{\alpha,p}=\left(\int_{\mathbb{R}^{2}}( \nabla u ^2+ u ^2)dx-\alpha(\int_{\mathbb{R}^{2}} u ^pdx)^{2/p}\right)^{1/2}\end{align*} where $0\leq\alpha2$ and $0\leq\alpha
Gradient Weyl-Ricci Soliton, Cornelia-Livia Bejan, Şemsi̇ Eken Meri̇ç, Erol Kiliç
Gradient Weyl-Ricci Soliton, Cornelia-Livia Bejan, Şemsi̇ Eken Meri̇ç, Erol Kiliç
Turkish Journal of Mathematics
The classical notion of gradient Ricci soliton is extended here to the gradient Weyl-Ricci soliton. A Weyl structureofthebasemanifold M is lifted to its tangent bundle TM, by using the Sasaki metric. We give some necessary and sufficient conditions such that the Weyl structure on TM to be a gradient Weyl-Ricci soliton.
A New Solution To The Discontinuity Problem On Metric Spaces, Ufuk Çeli̇k, Ni̇hal Özgür
A New Solution To The Discontinuity Problem On Metric Spaces, Ufuk Çeli̇k, Ni̇hal Özgür
Turkish Journal of Mathematics
We study on the Rhoades' question concerning the discontinuity problem at fixed point for a self-mapping T of a metric space. We obtain a new solution to this question. Our result generalizes some recent theorems existing in the literature and implies the uniqueness of the fixed point. However, there are also cases where the fixed point set of a self-mapping contains more than 1 element. Therefore, by a geometric point of view, we extend the Rhoades' question to the case where the fixed point set is a circle. We also give a solution to this extended version.
An Extragradient Algorithm For Split Generalized Equilibrium Problem And The Set Of Fixed Points Ofquasi-$\Phi $-Nonexpansive Mappings In Banach Spaces, Olawale Oyewole, Oluwatosin Mewomo, Lateef Jolaoso, Safeer Hussain Khan
An Extragradient Algorithm For Split Generalized Equilibrium Problem And The Set Of Fixed Points Ofquasi-$\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 …
A Study On Horadam Hybrid Numbers, Tuncay Deni̇z Şentürk, Göksal Bi̇lgi̇ci̇, Ahmet Daşdemi̇r, Zafer Ünal
A Study On Horadam Hybrid Numbers, Tuncay Deni̇z Şentürk, Göksal Bi̇lgi̇ci̇, Ahmet Daşdemi̇r, Zafer Ünal
Turkish Journal of Mathematics
In this paper, we study Horadam hybrid numbers. For these numbers, we give the exponential generating function, Poisson generating function, generating matrix, Vajda's, Catalan's, Cassini's, and d'Ocagne's identities. In addition, we offer Honsberger formula, general bilinear formula, and some summation formulas for these numbers.
Abstract Korovkin-Type Theorems In The Filter Setting With Respect To Relative Uniform Convergence, Antonio Boccuto, Kami̇l Demi̇rci̇, Sevda Yildiz
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.
A Semi-Markovian Renewal Reward Process With $\Gamma(G)$ Distributed Demand, Asli Bektaş Kamişlik, Büşra Alakoç, Tülay Kesemen, Tahi̇r Khani̇yev
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 $X(t)$.
On A Three-Dimensional Solvable System Of Difference Equations, Yacine Halim, Massaoud Berkal, Amira Khelifa
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.
On Geometric Applications Of Quaternions, Burcu Bektaş Demi̇rci̇, Nazim Aghayev
On Geometric Applications Of Quaternions, Burcu Bektaş Demi̇rci̇, Nazim Aghayev
Turkish Journal of Mathematics
Quaternions have become a popular and powerful tool in various engineering fields, such as robotics, image and signal processing, and computer graphics. However, classical quaternions are mostly used as a representation of rotation of a vector in $3$-dimensions, and connection between its geometric interpretation and algebraic structures is still not well-developed and needs more improvements. In this study, we develop an approach to understand quaternions multiplication defining subspaces of quaternion $\mathbb{H}$, called as $\mbox{Plane}(N)$ and $\mbox{Line}(N)$, and then, we observe the effects of sandwiching maps on the elements of these subspaces. Finally, we give representations of some transformations in geometry …
Solvability And Maximal Regularity Results For A Differential Equation With Diffusion Coefficient, Kordan Ospanov, Adilet Yesbayev
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.
Bilateral-Type Solutions To The Fixed-Circle Problem With Rectified Linear Units Application, Ni̇hal Taş
Bilateral-Type Solutions To The Fixed-Circle Problem With Rectified Linear Units Application, Ni̇hal Taş
Turkish Journal of Mathematics
In this paper, we prove new fixed-circle (resp. fixed-disc) results using the bilateral type contractions on a metric space. To do this, we modify some known contractive conditions called the Jaggi-type bilateral contraction and the Dass-Gupta type bilateral contraction. We give some examples to show the validity of our obtained results. Also, we construct an application to rectified linear units activation functions used in the neural networks. This application shows the importance of studying "fixed-circle problem".
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.
On Lyapunov-Type Inequalities For Boundary Value Problems Of Fractional Caputo-Fabrizio Derivative, Şuayi̇p Toprakseven
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.
Remarks On The One-Dimensional Sloshing Problem Involving The $P$-Laplacian Operator, Wei-Chuan Chen, Yanhsiou Cheng
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.
On Holomorphic Poly-Norden Manifolds, Çağri Karaman, Zühre Topuz
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.
Some Results On Prime Rings With Multiplicative Derivations, Gurninder Singh Sandhu, Di̇dem Karalarlioğlu Camci
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 …
On The Variational Curves Due To The Ed-Frame Field In Euclidean 4-Space, Muradi̇ye Çi̇mdi̇ker, Yasi̇n Ünlütürk
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.
An Analytical Investigatıon On Starlikeness And Convexity Properties For Hypergeometric Functions, İsmet Yildiz, Alaatti̇n Akyar
An Analytical Investigatıon On Starlikeness And Convexity Properties For Hypergeometric Functions, İsmet Yildiz, Alaatti̇n Akyar
Turkish Journal of Mathematics
In this study, we analytically investigate hypergeometric functions having some properties such as convexity and starlike. We fundamentally focus on obtaining desired conditions on the parameters \(a,b\), and $c$ in order that a hypergeometric function to be in various subclasses of starlike and convex functions of order \(\alpha=2^{-r}\) and order \(\alpha=2^{-r}\) type $\beta=2^{-1}$, with $r$ is a positive integer.
Units And 2-Class Field Towers Of Some Multiquadratic Number Fields, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini, Abdelmalek Azizi
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.
On 3-Dimensional Almost Einstein Manifolds With Circulant Structures, Iva Dokuzova
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 …
On Ulam's Type Stability Criteria For Fractional Integral Equations Including Hadamard Type Singular Kernel, Yasemi̇n Başci, Süleyman Öğrekçi̇, Adi̇l Misir
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.
Asymptotic Socle Behaviors For Cones Over Curves In Positive Characteristic, Jinjia Li
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 $I$.
Characterizations Of Dual Curves And Dual Focal Curves In Dual Lorentzian Space $ D^{3}_{1} $, Sareh Mehdizadeh Gilani, Nemat Abazari, Yusuf Yayli
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.
On Some Sums At The $A$-Points Of The $K$-Th Derivatives Of The Dirichlet $L$-Functions, Mohammed Mekkaoui, Abdallah Derbal, Kamel Mazhouda
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
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
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