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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.
The Cohomological Structure Of Fixed Point Set For Pro-Torus Actions On Compact Spaces, Mehmet Onat
The Cohomological Structure Of Fixed Point Set For Pro-Torus Actions On Compact Spaces, Mehmet Onat
Turkish Journal of Mathematics
In this paper, we study the relationships between the cohomological structure of a space and that of the fixed point set of a finite dimensional pro-torus action on the space.
When Is A Permutation Of The Set $\Z^N$ (Resp. $\Z_P^N$, $P$ Prime) An Automorphism Of The Group $\Z^N$ (Resp. $\Z_P^N$)?, Ben-Eben De Klerk, Johan H. Meyer
When Is A Permutation Of The Set $\Z^N$ (Resp. $\Z_P^N$, $P$ Prime) An Automorphism Of The Group $\Z^N$ (Resp. $\Z_P^N$)?, Ben-Eben De Klerk, Johan H. Meyer
Turkish Journal of Mathematics
For a given positive integer $n$, the structure, i.e. the number of cycles of various lengths, as well as possible chains, of the automorphisms of the groups $(\Z^n, +)$ and $(\Z_p^n,+)$, \ $p$ prime, is studied. In other words, necessary and sufficient conditions on a bijection $f : A \ra A$, where $ A $ is countably infinite (alternatively, of order $p^n$), are determined so that $A$ can be endowed with a binary operation $*$ such that $(A,*)$ is a group isomorphic to $(\Z^n,+)$ (alternatively, $(\Z_p^n,+)$) and such that $f\in \Aut(A)$.
Some Characterizations Of Right $C$-Regularity And $(B,C)$-Inverse, Ruju Zhao, Hua Yao, Long Wang, Junchao Wei
Some Characterizations Of Right $C$-Regularity And $(B,C)$-Inverse, Ruju Zhao, Hua Yao, Long Wang, Junchao Wei
Turkish Journal of Mathematics
Let $R$ be a ring and $a,b,c\in R$. We give a novel characterization of group inverses (resp. EP elements) by the properties of right (resp. left ) $c$-regular inverses of $a$ and discuss the relation among the strongly left $(b,c)$-invertibility of $a$, the right $ca$-regularity of $b$, and the $(b,c)$-invertibility of $a$. Finally, we investigate the sufficient and necessary condition for a ring to be a strongly left min-Abel ring by means of the $(b,c)$-inverse of $a$.
On The Solution Of An Inverse Sturm-Liouville Problem With A Delay And Eigenparameter-Dependent Boundary Conditions, Seyfollah Mosazadeh
On The Solution Of An Inverse Sturm-Liouville Problem With A Delay And Eigenparameter-Dependent Boundary Conditions, Seyfollah Mosazadeh
Turkish Journal of Mathematics
In this paper, a boundary value problem consisting of a delay differential equation of the Sturm-Liouville type with eigenparameter-dependent boundary conditions is investigated. The asymptotic behavior of eigenvalues is studied and the parameter of delay is determined by eigenvalues. Then we obtain the connection between the potential function and the canonical form of the characteristic function.
Closed Range Properties Of Li-Steviç Integral-Type Operators Between Bloch-Type Spaces And Their Essential Norms, Maryam Mohammadi Pirasteh, Nasrin Eghbali, Amir Hossein Sanatpour
Closed Range Properties Of Li-Steviç Integral-Type Operators Between Bloch-Type Spaces And Their Essential Norms, Maryam Mohammadi Pirasteh, Nasrin Eghbali, Amir Hossein Sanatpour
Turkish Journal of Mathematics
We investigate closed range properties of certain integral-type operators introduced by Li and Steviç. The operators are considered between Bloch-type spaces. We also give the essential norm of such operators. Our results are given in a general setting and we also give the essential norm of Li-Steviç integral-type operators between other well-known spaces of analytic functions.
Conditional Expectation Type Operators And Modular Inequalities, Dah-Chin Luor
Conditional Expectation Type Operators And Modular Inequalities, Dah-Chin Luor
Turkish Journal of Mathematics
In this paper we discuss the connection between conditional expectation type operators and integral operators. A variant of Schur's lemma is established and we obtain modular inequalities for a class of conditional expectation type operators.
Curves Whose Pseudo Spherical Indicatrices Are Elastic, Ahmet Yücesan, Gözde Özkan Tükel, Tunahan Turhan
Curves Whose Pseudo Spherical Indicatrices Are Elastic, Ahmet Yücesan, Gözde Özkan Tükel, Tunahan Turhan
Turkish Journal of Mathematics
The pseudo spherical indicatrix of a curve in Minkowski $3$-space emerges as three types: the pseudo spherical tangent indicatrix, principal normal indicatrix, and binormal indicatrix of the curve. The pseudo spherical tangent, principal normal, and binormal indicatrix of a regular curve may be positioned on De Sitter $2$-space (pseudo sphere), pseudo hyperbolic 2-space, and two-dimensional null cone in terms of causal character of the curve. In this paper, we separately derive Euler-Lagrange equations of all pseudo spherical indicatrix elastic curves in terms of the causal character of a curve in Minkowski $3$-space. Then we give some results of solutions of …
Jackson And\ Stechkin Type Inequalities Of Trigonometricapproximation In $A_{W,\Vartheta }^{P,Q(\Cdot )}$, Ahmet Hamdi̇ Avşar, Hüseyi̇n Koç
Jackson And\ Stechkin Type Inequalities Of Trigonometricapproximation In $A_{W,\Vartheta }^{P,Q(\Cdot )}$, Ahmet Hamdi̇ Avşar, Hüseyi̇n Koç
Turkish Journal of Mathematics
In this paper, we study Jackson and Stechkin type theorems of trigonometric polynomial approximation in the space $A_{w,\vartheta }^{p,q(\cdot )}$ by considering a modulus of smoothness defined by virtue of the Steklov operator.
On Spanning Sets And Generators Of Near-Vector Spaces, Karin-Therese Howell, Sogo Pierre Sanon
On Spanning Sets And Generators Of Near-Vector Spaces, Karin-Therese Howell, Sogo Pierre Sanon
Turkish Journal of Mathematics
In this paper we study the quasi-kernel of certain constructions of near-vector spaces and the span of a vector. We characterize those vectors whose span is one-dimensional and those that generate the whole space.
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.
Generalized Metric $N$-Leibniz Algebras And Generalized Orthogonal Representation Of Metric Lie Algebras, Rong Tang, Lina Song
Generalized Metric $N$-Leibniz Algebras And Generalized Orthogonal Representation Of Metric Lie Algebras, Rong Tang, Lina Song
Turkish Journal of Mathematics
We introduce the notion of a generalized metric $n$-Leibniz algebra and show that there is a one-to-one correspondence between generalized metric $n$-Leibniz algebras and faithful generalized orthogonal representations of metric Lie algebras (called Lie triple datas). We further show that there is also a one-to-one correspondence between generalized orthogonal derivations (resp. generalized orthogonal automorphisms) on generalized metric $n$-Leibniz algebras and Lie triple data.
Harmonic Quadrangle In Isotropic Plane, Ema Jurkin, Marija Simic Horvath, Vladimir Volenec, Jelena Beban-Brkic
Harmonic Quadrangle In Isotropic Plane, Ema Jurkin, Marija Simic Horvath, Vladimir Volenec, Jelena Beban-Brkic
Turkish Journal of Mathematics
The concept of the harmonic quadrangle and the associated Brocard points are introduced and investigated in the isotropic plane by employing suitable analytic methods.
On Matrix Rings With The Sip And The Ads, Fi̇gen Takil Mutlu
On Matrix Rings With The Sip And The Ads, Fi̇gen Takil Mutlu
Turkish Journal of Mathematics
In this paper, matrix rings with the summand intersection property (SIP) and the absolute direct summand (ads) property (briefly, $SA$) are studied. A ring $R$ has the right SIP if the intersection of two direct summands of $R$ is also a direct summand. A right $R$-module $M$ has the ads property if for every decomposition $M=A\oplus B$ of $M$ and every complement $C$ of $A$ in $M$, we have $M=A\oplus C$. It is shown that the trivial extension of $R$ by $M$ has the SA if and only if $R$ has the SA, $M$ has the ads, and $(1-e)Me=0$ for …
Certain Strongly Clean Matrices Over Local Rings, Tuğçe Pekacar Çalci, Huanyin Chen
Certain Strongly Clean Matrices Over Local Rings, Tuğçe Pekacar Çalci, Huanyin Chen
Turkish Journal of Mathematics
We are concerned about various strongly clean properties of a kind of matrix subrings $L_{(s)}(R)$ over a local ring $R$. Let $R$ be a local ring, and let $s\in C(R)$. We prove that $A\in L_{(s)}(R)$ is strongly clean if and only if $A$ or $I_2-A$ is invertible, or $A$ is similar to a diagonal matrix in $L_{(s)}(R)$. Furthermore, we prove that $A\in L_{(s)}(R)$ is quasipolar if and only if $A\in GL_2(R)$ or $A\in L_{(s)}(R)^{qnil}$, or $A$ is similar to a diagonal matrix $\left( \begin{array}{cc} \lambda&0\\ 0&\mu \end{array} \right)$ in $L_{(s)}(R)$, where $\lambda\in J(R)$, $\mu\in U(R)$ or $\lambda\in U(R)$, $\mu\in J(R)$, …
Existence Of Solution For Some Two-Point Boundary Value Fractional Differential Equations, Kenneth Ifeanyi Isife
Existence Of Solution For Some Two-Point Boundary Value Fractional Differential Equations, Kenneth Ifeanyi Isife
Turkish Journal of Mathematics
Using a fixed point theorem, we establish the existence of a solution for a class of boundary value fractional differential equation. Secondly, we will adopt the method of successive approximations to obtain an approximate solution to our problem. Furthermore, using the Laplace transform technique, an explicit solution to a particular case of our problem is obtained. Finally, some examples are given to illustrate our results.
Transversal Lightlikesubmanifolds Of Metallic Semi-Riemannian Manifolds, Feyza Esra Erdoğan
Transversal Lightlikesubmanifolds Of Metallic Semi-Riemannian Manifolds, Feyza Esra Erdoğan
Turkish Journal of Mathematics
The main purpose of the present paper is to study the geometry of transversal lightlike submanifolds and radical transversal lightlike submanifolds of metallic semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be a metric connection. We also obtain characterization of transversal lightlike submanifolds of metallic semi-Riemannian manifolds. Finally, we give two examples.
On Rectifying Curves In Euclidean 3-Space, Sharief Deshmukh, Bang-Yen Chen, Sana Hamoud Alshammari
On Rectifying Curves In Euclidean 3-Space, Sharief Deshmukh, Bang-Yen Chen, Sana Hamoud Alshammari
Turkish Journal of Mathematics
First, we study rectifying curves via the dilation of unit speed curves on the unit sphere $S^{2}$ in the Euclidean space $\mathbb E^3$. Then we obtain a necessary and sufficient condition for which the centrode $d(s)$ of a unit speed curve $\alpha(s)$ in $\mathbb E^3$ is a rectifying curve to improve a main result of \cite{cd05}. Finally, we prove that if a unit speed curve $\alpha(s)$ in $\mathbb E^3$ is neither a planar curve nor a helix, then its dilated centrode $\beta(s)=\rho(s) d(s)$, with dilation factor ${\rho}$, is always a rectifying curve, where $\rho$ is the radius of curvature of …
A New Approach To $H$-Supplemented Modules Via Homomorphisms, Ali Reza Moniri Hamzekolaee, Abdullah Harmanci, Yahya Talebi, Burcu Üngör
A New Approach To $H$-Supplemented Modules Via Homomorphisms, Ali Reza Moniri Hamzekolaee, Abdullah Harmanci, Yahya Talebi, Burcu Üngör
Turkish Journal of Mathematics
The class of $H$-supplemented modules, which is a nice generalization of that of lifting modules, has been studied extensively in the last decade. As the concept of homomorphisms plays an important role in module theory, we are interested in $H$-supplemented modules relative to homomorphisms. Let $R$ be a ring, $M$ a right $R$-module, and $S=$ End$_{R}(M)$. We say that $M$ is endomorphism $H$-supplemented (briefly, $E$-$H$-supplemented) provided that for every $f\in S$ there exists a direct summand $D$ of $M$ such that $Imf+X=M$ if and only if $D+X=M$ for every submodule $X$ of $M$. In this paper, we deal with the …
Parametric Nondifferentiable Multiobjective Fractional Programmingunder $(B,\Psi ,\Phi ,\Rho )$-Univexity, Tadeusz Antczak, Ram Verma
Parametric Nondifferentiable Multiobjective Fractional Programmingunder $(B,\Psi ,\Phi ,\Rho )$-Univexity, Tadeusz Antczak, Ram Verma
Turkish Journal of Mathematics
In this paper, we are concerned with optimality conditions and duality results for nondifferentiable multiobjective fractional programming problems. Parametric necessary optimality conditions are established for such vector optimization problems in which each component of the involved functions is locally Lipschitz. Further, under the introduced concept of nondifferentiable $(b,\Psi ,\Phi ,\rho )$-univexity, the parametric sufficient optimality conditions are established for a new class of nonconvex multiobjective fractional programming problems. Furthermore, for the considered multiobjective fractional programming problem, its parametric vector dual problem in the sense of Schaible is defined. Then several duality theorems are also established under $(b,\Psi ,\Phi ,\rho )$% …