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Articles 1081 - 1110 of 2595
Full-Text Articles in Mathematics
Properties In $L_P$ Of Root Functions For A Nonlocal Problem With Involution, Leonid Kritskov, Makhmud Sadybekov, Abdizhahan Sarsenbi
Properties In $L_P$ Of Root Functions For A Nonlocal Problem With Involution, Leonid Kritskov, Makhmud Sadybekov, Abdizhahan Sarsenbi
Turkish Journal of Mathematics
The spectral problem $-u''(x)+\alpha u''(-x)=\lambda u(x)$, $-1$%lt; $x$ < $1$, with nonlocal boundary conditions $u(-1)=\beta u(1)$, $u'(-1)=u'(1)$, is studied in the spaces $L_p(-1,1)$ for any $\alpha\in (-1,1)$ and $\beta\ne\pm 1$. It is proved that if $r=\sqrt{(1-\alpha)/(1+\alpha)}$ is irrational then the system of its eigenfunctions is complete and minimal in $L_p(-1,1)$ for any $p>1$, but does not form a basis. In the case of a rational value of $r$, the way of supplying this system with associated functions is specified to make all the root functions a basis in $L_p(-1,1)$.
On Linear Dynamics Of Sets Of Operators, Mohamed Amouch, Otmane Benchiheb
On Linear Dynamics Of Sets Of Operators, Mohamed Amouch, Otmane Benchiheb
Turkish Journal of Mathematics
Let $X$ be a complex topological vector space with $dim(X)>1$ and $\mathcal{B}(X)$ the set of all continuous linear operators on $X$. The concept of hypercyclicity for a subset of $\mathcal{B}(X)$ was introduced in [1]. In this work, we introduce the notion of hypercyclic criterion for a subset of $\mathcal{B}(X)$. We extend some results known for a single operator and $C_0$-semigroup to a subset of $\mathcal{B}(X)$ and we give applications for $C$-regularized groups of operators.
On Product Complex Finsler Manifolds, Hongchuan Xia, Qian Wei
On Product Complex Finsler Manifolds, Hongchuan Xia, Qian Wei
Turkish Journal of Mathematics
Let $(M, F)$ be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds $(M_1, F_1)$ and $(M_2, F_2)$ with $F=\sqrt{f(K, H)}$ and $K=F_1^2$, $H=F_2^2$. In this paper, we prove that $(M, F)$ is a weakly Käahler-Finsler (resp. weakly complex Berwald) manifold if and only if $(M_1, F_1)$ and $(M_2, F_2)$ are both weakly Kähler-Finsler (resp. weakly complex Berwald) manifolds, which is independent of the choice of function $f$. Meanwhile, we prove that $(M, F)$ is a complex Landsberg manifold if and only if either $(M_1, F_1)$ and $(M_2, F_2)$ are both complex Landsberg manifolds and $f=c_1K+c_2H$ with …
Properties Of A Generalized Class Of Analytic Functions With Coefficient Inequality, Ben Wongsaijai, Nattakorn Sukantamala
Properties Of A Generalized Class Of Analytic Functions With Coefficient Inequality, Ben Wongsaijai, Nattakorn Sukantamala
Turkish Journal of Mathematics
Let $(\beta_n)_{n\ge 2}$ be a sequence of nonnegative real numbers and $\delta$ be a positive real number. We introduce the subclass $\mathcal{A}(\beta_n,\delta)$ of analytic functions, with the property that the Taylor coefficients of the function $f$ satisfies $\sum_{n\ge2}^{\infty}\beta_n a_n \le \delta$, where $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$. The class $\mathcal{A}(\beta_n,\delta)$ contains nonunivalent functions for some choices of $(\beta_n)_{n\ge 2}$. In this paper, we provide some general properties of functions belonging to the class $\mathcal{A}(\beta_n,\delta)$, such as the radii of univalence, distortion theorem, and invariant property. Furthermore, we derive the best approximation of an analytic function in such class by using the semiinfinite quadratic programming. …
Some General Results On Fractional Banach Sets, Faruk Özger
Some General Results On Fractional Banach Sets, Faruk Özger
Turkish Journal of Mathematics
The gamma function which is expressed by an improper integral is used to establish the fractional difference operators and fractional Banach sets. In this study, we achieve some comprehensive and complementary results related to characterizations of the matrix classes of fractional Banach sets. We also obtain some identities or inequalities for the Hausdorff measure of noncompactness of the corresponding matrix operators, and finally find the necessary and sufficient conditions for those matrix operators to be compact.
A Bernstein-Type Theorem For $\Xi$-Submanifolds Withflat Normal Bundle In The Euclidean Spaces, Xu-Yong Jiang, He-Jun Sun, Peibiao Zhao
A Bernstein-Type Theorem For $\Xi$-Submanifolds Withflat Normal Bundle In The Euclidean Spaces, Xu-Yong Jiang, He-Jun Sun, Peibiao Zhao
Turkish Journal of Mathematics
$\xi$-Submanifolds in the Euclidean spaces are a natural extension of self-shrinkers and a generalization of $\lambda$-hypersurfaces. Moreover, $\xi$-submanifolds are expected to take the place of submanifolds with parallel mean curvature vector. In this paper, we establish a Bernstein-type theorem for $\xi$-submanifolds in the Euclidean spaces. More precisely, we prove that an $n$-dimensional smooth graphic $\xi$-submanifold with flat normal bundle in $\mathbb{R}^{n+p}$ is an affine $n$-plane.
Converse Theorems In Lyapunov's Second Method And Applications For Fractional Order Systems, Javier Gallegos, Manuel Duarte-Mermoud
Converse Theorems In Lyapunov's Second Method And Applications For Fractional Order Systems, Javier Gallegos, Manuel Duarte-Mermoud
Turkish Journal of Mathematics
We establish a characterization of the Lyapunov and Mittag-Leffler stability through (fractional) Lyapunov functions, by proving converse theorems for Caputo fractional order systems. A hierarchy for the Mittag-Leffler order convergence is also proved which shows, in particular, that fractional differential equation with derivation order lesser than one cannot be exponentially stable. The converse results are then applied to show that if an integer order system is (exponentially) stable, then its corresponding fractional system, obtained from changing its differentiation order, is (Mittag-Leffler) stable. Hence, available integer order control techniques can be disposed to control nonlinear fractional systems. Finally, we provide examples …
On The Cover Ideals Of Chordal Graphs, Nursel Erey
On The Cover Ideals Of Chordal Graphs, Nursel Erey
Turkish Journal of Mathematics
The independence complex of a chordal graph is known to be shellable which is equivalent to the fact that cover ideal of a chordal graph has linear quotients. We use this result to obtain recursive formulas for the Betti numbers of cover ideals of chordal graphs. Moreover, we give a new proof of such result which yields different shellings of the independence complex.
A Circulant Functional Equation For The Additive Function And Its Stability, Vichian Laohakosol, Watcharapon Pimsert, Kanet Ponpetch
A Circulant Functional Equation For The Additive Function And Its Stability, Vichian Laohakosol, Watcharapon Pimsert, Kanet Ponpetch
Turkish Journal of Mathematics
A general solution of a matrix functional equation involving circulant matrices of the additive function is determined, and its stability is established.
On The Chebyshev Coefficients For A General Subclass Of Univalentfunctions, Şahsene Altinkaya, Si̇bel Yalçin Tokgöz
On The Chebyshev Coefficients For A General Subclass Of Univalentfunctions, Şahsene Altinkaya, Si̇bel Yalçin Tokgöz
Turkish Journal of Mathematics
In this work, considering a general subclass of univalent functions and using the Chebyshev polynomials, we obtain coefficient expansions for functions in this class.
Linear Methods Of Summing Fourier Series And Approximation In Weighted Orliczspaces, Sadulla Jafarov
Linear Methods Of Summing Fourier Series And Approximation In Weighted Orliczspaces, Sadulla Jafarov
Turkish Journal of Mathematics
In the present work, we investigate estimates of the deviations of the periodic functions from the linear operators constructed on the basis of its Fourier series in reflexive weighted Orlicz spaces with Muckenhoupt weights. In particular, the orders of approximation of Zygmund and Abel-Poisson means of Fourier trigonometric series were estimated by the $k-th$~modulus of smoothness in reflexive weighted Orlicz spaces with Muckenhoupt weights.
The Diameter Vulnerability Of The Generalized Petersen Graph ${Gp[Tk,K]}$, Gülnaz Boruzanli Eki̇nci̇, John Baptist Gauci
The Diameter Vulnerability Of The Generalized Petersen Graph ${Gp[Tk,K]}$, Gülnaz Boruzanli Eki̇nci̇, John Baptist Gauci
Turkish Journal of Mathematics
The diameter of a graph gives the length of the longest path among all the shortest paths between any two vertices of the graph, and the diameter vulnerability problem measures the change in the diameter upon the deletion of edges. In this paper we determine the diameter vulnerability of the generalized Petersen graph $GP[tk,k]$, for integers $t\geq 2$ and $k\geq 1$, and show that (except for some small cases) the diameter remains unchanged upon the deletion of one edge. This work contributes towards a solution of the well-known $(\Delta, D, D', s)$-problem, which attempts to find large graphs with maximum …
Construction Of The Second Hankel Determinant For A New Subclass Ofbi-Univalent Functions, Şahsene Altinkaya, Si̇bel Yalçin Tokgöz
Construction Of The Second Hankel Determinant For A New Subclass Ofbi-Univalent Functions, Şahsene Altinkaya, Si̇bel Yalçin Tokgöz
Turkish Journal of Mathematics
In this paper, we will discuss a newly constructed subclass of bi-starlike functions. Furthermore, we establish bounds for the coefficients and get the second Hankel determinant for the class $S_{\Sigma }(\alpha ,\beta ).$
Description Of Invariant Subspaces In Terms Of Berezin Symbols, Suna Saltan
Description Of Invariant Subspaces In Terms Of Berezin Symbols, Suna Saltan
Turkish Journal of Mathematics
We consider the stretching operator $\left( T_{w}f\right) \left( z\right) =f(wz)$ and the multiple shift operator $S^{n}f=z^{n}f$ on the Hardy spaces $% H^{p}(\mathbb{D})$ $\left( 1\leq p
Free Modules And Crossed Modules Of $R$-Algebroids, Osman Avcioğlu, İbrahi̇m İlker Akça
Free Modules And Crossed Modules Of $R$-Algebroids, Osman Avcioğlu, İbrahi̇m İlker Akça
Turkish Journal of Mathematics
In this paper, first, we construct the free modules and precrossed modules of $R$-algebroids. Then we introduce the Peiffer ideal of a precrossed module and use it to construct the free crossed module.
Generalization Of The Cayley Transform In 3d Homogeneous Geometries, Zlatko Erjavec
Generalization Of The Cayley Transform In 3d Homogeneous Geometries, Zlatko Erjavec
Turkish Journal of Mathematics
The Cayley transform maps the unit disk onto the upper half-plane, conformally and isometrically. In this paper, we generalize the Cayley transform in three-dimensional homogeneous geometries which are fiber bundles over the hyperbolic plane. Obtained generalizations are isometries between existing models in corresponding homogeneous geometries. Particularly, constructed isometry between two models of { $\widetilde{SL(2,\mathbb{R})}$} geometry is nontrivial and enables comparison and transfer of known and even future results between these two models.
Trigonometric Expressions For Infinite Series Involving Binomial Coefficients, Nadia Li
Trigonometric Expressions For Infinite Series Involving Binomial Coefficients, Nadia Li
Turkish Journal of Mathematics
By means of the hypergeometric series approach, we present a new proof of Sun's conjecture on trigonometric series, which is simpler than the original one due to Sun and Meng. Several further infinite series identities are shown as examples.
On The Asymptotic Behavior Of Solution Of Certain Systems Of Volterra Equations, Ewa Schmeidel, Malgorzata Zdanowicz
On The Asymptotic Behavior Of Solution Of Certain Systems Of Volterra Equations, Ewa Schmeidel, Malgorzata Zdanowicz
Turkish Journal of Mathematics
This paper is concerned with the asymptotic property of the solution of a system of the linear Volterra difference equations. The criterion for the existence of a solution of the considered system that is asymptotically equivalent to a given sequence is established. %The results generalize some recent results. The results presented here improve and generalize the results published by Diblik et al. Unlike in those works, here periodicity of the nonhomogeneous term of the equation is not assumed. Examples illustrate the obtained results.
Almost Paracontact Structures Obtained From $G_{2(2)}^*$ Structures, Nüli̇fer Özdemi̇r, Şi̇ri̇n Aktay, Mehmet Solgun
Almost Paracontact Structures Obtained From $G_{2(2)}^*$ Structures, Nüli̇fer Özdemi̇r, Şi̇ri̇n Aktay, Mehmet Solgun
Turkish Journal of Mathematics
In this paper, we construct almost paracontact metric structures by using the fundamental 3-forms of manifolds with $G_{2(2)}^*$ structures. The existence of certain almost paracontact metric structures is investigated due to the properties of the 2-fold vector cross-product. Furthermore, we give some relations between the classes of $G_{2(2)}^*$ structures and almost paracontact metric structures.
On Hochstadt--Lieberman Theorem For Impulsive Sturm-Liouville Problems With Boundary Conditions Polynomially Dependent On The Spectral Parameter, Seyfollah Mosazadeh, Aliasghar Jodayree Akbarfam
On Hochstadt--Lieberman Theorem For Impulsive Sturm-Liouville Problems With Boundary Conditions Polynomially Dependent On The Spectral Parameter, Seyfollah Mosazadeh, Aliasghar Jodayree Akbarfam
Turkish Journal of Mathematics
In the present paper, we consider an inverse problem for the Sturm-Liouville operator with a finite number of discontinuities at interior points and boundary conditions polynomially dependent on the spectral parameter on an arbitrary finite interval, and prove the Hochstadt-Lieberman-type theorem for this problem.
Several Hardy-Type Inequalities With Weights Related To Baouendi--Grushinoperators, Abdullah Yener
Several Hardy-Type Inequalities With Weights Related To Baouendi--Grushinoperators, Abdullah Yener
Turkish Journal of Mathematics
In this paper we shall prove several weighted $L^{p}$ Hardy-type inequalities associated to the Baouendi-Grushin-type operators $\Delta _{\gamma }=\Delta _{x}+\left\vert x\right\vert ^{2\gamma }\Delta _{y},$ where $\Delta _{x}$ and $\Delta _{y}$ are the classical Laplace operators in the variables $x\in \mathbb{R}^{n}$ and $y\in \mathbb{R}^{k},$ respectively, and $\gamma $ is a positive real number.
Linearized Four-Step Implicit Scheme For Nonlinear Parabolic Interface Problems, Matthew Olayiwola Adewole, Victor Folarin Payne
Linearized Four-Step Implicit Scheme For Nonlinear Parabolic Interface Problems, Matthew Olayiwola Adewole, Victor Folarin Payne
Turkish Journal of Mathematics
We present the solution of a second-order nonlinear parabolic interface problem on a quasiuniform triangular finite element with a linearized four-step implicit scheme used for the time discretization. The convergence of the scheme in $L^2$-norm is established under certain regularity assumptions using interpolation and elliptic projection operators. A numerical experiment is presented to support the theoretical result. It is assumed that the interface cannot be fitted exactly.
Radii Of Uniform Convexity Of Some Special Functions, İbrahi̇m Aktaş, Evri̇m Toklu, Hali̇t Orhan
Radii Of Uniform Convexity Of Some Special Functions, İbrahi̇m Aktaş, Evri̇m Toklu, Hali̇t Orhan
Turkish Journal of Mathematics
In this investigation our main aim is to determine the radii of uniform convexity of selected normalized $ q $-Bessel and Wright functions. Here we consider six different normalized forms of $ q $-Bessel functions and we apply three different kinds of the normalization of the Wright function. We also show that the obtained radii are the smallest positive roots of some functional equations.
Inequalities For Submanifolds Of Sasaki-Like Statistical Manifolds, Hülya Bostan Ayti̇mur, Ci̇han Özgür
Inequalities For Submanifolds Of Sasaki-Like Statistical Manifolds, Hülya Bostan Ayti̇mur, Ci̇han Özgür
Turkish Journal of Mathematics
We consider statistical submanifolds in Sasaki-like statistical manifolds. We give some examples of invariant and antiinvariant submanifolds of Sasaki-like statistical manifolds. We prove Chen-like inequality involving scalar curvature and Chen-Ricci inequality for these kinds of submanifolds.
Spectrum And Scattering Function Of The Impulsive Discrete Dirac Systems, Elgiz Bairamov, Şeyda Solmaz
Spectrum And Scattering Function Of The Impulsive Discrete Dirac Systems, Elgiz Bairamov, Şeyda Solmaz
Turkish Journal of Mathematics
In this paper, we investigate analytical and asymptotic properties of the Jost solution and Jost function of the impulsive discrete Dirac equations. We also study eigenvalues and spectral singularities of these equations. Then we obtain characteristic properties of the scattering function of the impulsive discrete Dirac systems. Therefore, we find the Jost function, point spectrum, and scattering function of the unperturbed impulsive equations.
Inclusions And The Approximate Identities Of The Generalized Grand Lebesgue Spaces, Ahmet Turan Gürkanli
Inclusions And The Approximate Identities Of The Generalized Grand Lebesgue Spaces, Ahmet Turan Gürkanli
Turkish Journal of Mathematics
Let $\left( \Omega ,\sum ,\mu \right) $ and $\left( \Omega ,\sum ,v\right) $ be two finite measure spaces and let $L^{p),\theta }\left( \mu \right) $ and $L^{q),\theta }\left( v\right) $ be two generalized grand Lebesgue spaces $\left[ 9,10\right] ,$ where $1
Digital Topological Complexity Numbers, İsmet Karaca, Meli̇h İs
Digital Topological Complexity Numbers, İsmet Karaca, Meli̇h İs
Turkish Journal of Mathematics
The intersection of topological robotics and digital topology leads to us a new workspace. In this paper we introduce the new digital homotopy invariant digital topological complexity number $TC(X,\kappa)$ for digital images and give some examples and results about it. Moreover, we examine adjacency relations in the digital spaces and observe how $TC(X,\kappa)$ changes when we take a different adjacency relation in the digital spaces.
Existence And Nonexistence Of Global Solutions For Nonlinear Transmission Acoustic Problem, Akbar Aliyev, Sevda Isayeva
Existence And Nonexistence Of Global Solutions For Nonlinear Transmission Acoustic Problem, Akbar Aliyev, Sevda Isayeva
Turkish Journal of Mathematics
In this paper we consider a mixed problem for the nonlinear wave equations with transmission acoustic conditions, that is, the wave propagation over bodies consisting of two physically different types of materials, one of which is clamped. We prove the existence of a global solution. Under the condition of positive initial energy we show that the solution for this problem blows up in finite time.
Frequently Hypercyclic Weighted Backward Shifts On Spaces Of Real Analytic Functions, Berkay Anahtarci, Can Deha Kariksiz
Frequently Hypercyclic Weighted Backward Shifts On Spaces Of Real Analytic Functions, Berkay Anahtarci, Can Deha Kariksiz
Turkish Journal of Mathematics
We study frequent hypercyclicity in the case of weighted backward shift operators acting on locally convex spaces of real analytic functions. We obtain certain conditions on frequent hypercyclicity and linear chaoticity of these operators using dynamical transference principles and the frequent hypercyclicity criterion.
Ellipses And Similarity Transformations With Norm Functions, Ni̇hal Yilmaz Özgür
Ellipses And Similarity Transformations With Norm Functions, Ni̇hal Yilmaz Özgür
Turkish Journal of Mathematics
In this paper, we deal with a conjecture related to the images of ellipses (resp. circles) under similarities that are the special Möbius transformations. We consider ellipses (resp. circles) corresponding to any norm function (except in the Euclidean case) on the complex plane and examine some conditions to confirm this conjecture. Some illustrative examples are also given.