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2020

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Articles 961 - 990 of 1327

Full-Text Articles in Mathematics

A Generalization Of The Minkowski Distance And New Definitions Of The Central Conics, Harun Bariş Çolakoğlu Jan 2020

A Generalization Of The Minkowski Distance And New Definitions Of The Central Conics, Harun Bariş Çolakoğlu

Turkish Journal of Mathematics

In this paper, we give a generalization of the well-known Minkowski distance family in the $n$-dimensional Cartesian coordinate space. Then we consider three special cases of this family, which are also generalizations of the taxicab, Euclidean, and maximum metrics, respectively, and we determine some circle properties of them in the real plane. While we determine some properties of circles of these generalized distances, we discover a new definition of ellipses, and then we also determine a similar definition of hyperbolas, which will be new members among different metrical definitions of central conics in the Euclidean plane.

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Continuous Dependence Of Solutions For Damped Improved Boussinesq Equation, Sema Bayraktar, Şevket Gür Jan 2020

Continuous Dependence Of Solutions For Damped Improved Boussinesq Equation, Sema Bayraktar, Şevket Gür

Turkish Journal of Mathematics

In this paper, the initial-boundary value problem for a damped nonlinear improved Boussinesq equation is studied. A priori estimates for the solution of the equation are obtained in terms of initial data and coefficients of the problem. The continuous dependence of solutions on dispersive $(\delta)$ and $(r)$ and dissipative $(b)$ coefficients are established by multiplier method.

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Coefficient Estimates For The Class Of Quasi Q-Convex Functions, Osman Altintaş, Seher Meli̇ke Aydoğan Jan 2020

Coefficient Estimates For The Class Of Quasi Q-Convex Functions, Osman Altintaş, Seher Meli̇ke Aydoğan

Turkish Journal of Mathematics

In this paper we introduce and investigate the class of $ P_{q}(\lambda,\beta, A, B)$, which is called quasi q-starlike and quasi q-convex with respect to the values of the parameter $\lambda$. We give coefficient bounds estimates and the results for the main theorem.

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Approximation By Matrix Transforms In Weighted Orlicz Spaces, Sadulla Jafarov Jan 2020

Approximation By Matrix Transforms In Weighted Orlicz Spaces, Sadulla Jafarov

Turkish Journal of Mathematics

In this work the approximation problems of the functions by matrix transforms in weighted Orlicz spaces with Muckenhoupt weights are studied.We obtain the degree of approximation of functions belonging to Lipschitz class $Lip(\alpha ,M,\omega )$ through matrix transforms $% T_{n}^{\left( A\right) }(x,f)$,$~$and Nörlund means $N_{n}\left(x,f\right) ~$of their trigonometric Fourier series.

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On Extensions Of Two Results Due To Ramanujan, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris Jan 2020

On Extensions Of Two Results Due To Ramanujan, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris

Turkish Journal of Mathematics

The aim in this note is to provide a generalization of an interesting entry in Ramanujan's notebooks that relate sums involving the derivatives of a function $\varphi\left( t\right)$ evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating ${}_3F_2$ hypergeometric functions of argument equal to 2, recently obtained by Kim et. al. [Two results for the terminating ${}_3F_2$(2) with applications, Bulletin of the Korean Mathematical Society 2012; 49: 621-633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.

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The Formulization Of The Intrinsic Metric On The Added Sierpinski Triangle By Using The Code Representations, Aslihan İkli̇m Şen, Mustafa Saltan Jan 2020

The Formulization Of The Intrinsic Metric On The Added Sierpinski Triangle By Using The Code Representations, Aslihan İkli̇m Şen, Mustafa Saltan

Turkish Journal of Mathematics

To formulate the intrinsic metrics by using the code representations of the points on the classical fractals is an important research area since these formulas help to prove many geometrical and structural properties of these fractals. In various studies, the intrinsic metrics on the code set of the Sierpinski gasket, the Sierpinski tetrahedron, and the Vicsek (box) fractal are explicitly formulated. However, in the literature, there are not many works on the intrinsic metric that is obtained by the code representations of the points on fractals. Moreover, as seen in the studies on this subject, the contraction coefficients of the …

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Prolongations Of Isometric Actions To Vector Bundles, Hülya Kadioğlu Jan 2020

Prolongations Of Isometric Actions To Vector Bundles, Hülya Kadioğlu

Turkish Journal of Mathematics

In this paper, we define an isometry on a total space of a vector bundle $\mathbb{E}$ by using a given isometry on the base manifold $\mathbb{M}$. For this definition, we assume that the total space of the bundle is equipped with a special metric which has been introduced in one of our previous papers. We prove that the set of these derived isometries on $\mathbb{E}$ form an imbedded Lie subgroup $\tilde{G}$ of the isometry group $I(E)$. Using this new subgroup, we construct two different principal bundle structures based one on $\mathbb{E}$ and the other on the orbit space $\mathbb{E}/\tilde{G}$.

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Faber-Laurent Series In Variable Smirnov Classes, Dani̇yal İsrafi̇lzade, Eli̇fe Gürsel Jan 2020

Faber-Laurent Series In Variable Smirnov Classes, Dani̇yal İsrafi̇lzade, Eli̇fe Gürsel

Turkish Journal of Mathematics

In this work, the maximal convergence properties of partial sums of Faber-Laurent series in the variable exponent Smirnov classes of analytic functions defined on a doubly connected domain of the complex plane are investigated.

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The Existence And Compactness Of The Set Of Solutions For A Nonlinear Integrodifferential Equation In N Variables In A Banach Space, Huynh Thi Hoang Dung, Le Thi Phuong Ngoc, Nguyen Thanh Long Jan 2020

The Existence And Compactness Of The Set Of Solutions For A Nonlinear Integrodifferential Equation In N Variables In A Banach Space, Huynh Thi Hoang Dung, Le Thi Phuong Ngoc, Nguyen Thanh Long

Turkish Journal of Mathematics

The paper is devoted to the study of a nonlinear integrodifferential equation in N variables with values in a general Banach space. By applying fixed point theorems in a suitable Banach space under appropriate conditions for subsets to be relatively compact, we prove the existence and the compactness of theset of solutions.Inorder to illustrate the results,we give two examples.

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Regular Sequences In The Subrings Of C(X), Fariborz Azarpanah, Delavar Esmaeilvandi Jan 2020

Regular Sequences In The Subrings Of C(X), Fariborz Azarpanah, Delavar Esmaeilvandi

Turkish Journal of Mathematics

We show that the intermediate subalgebras between $C^*(X)$ and C(X) do not contain regular sequences with length $\geq$ 2. This shows that depth(A(X)) $\leq$ 1 for each intermediate subalgebra A(X) between $C^*(X)$ and C(X). Whenever an intermediate subalgebra A(X) is proper, i.e. A(X) $\neq$ C(X), we observe that the depth of A(X) is exactly 1. Using this, it turns out that depth($C^*(X)$) = 0 if and only if $X$ is a pseuodocompact almost $P$ -space. The regular sequences in the subrings of the form $I + \mathbb{R}$ of C(X), where $I$ is a $z$-ideal of C(X), are also investigated and …

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Discrete-Time Average-Cost Mean-Field Games On Polish Spaces, Naci̇ Saldi Jan 2020

Discrete-Time Average-Cost Mean-Field Games On Polish Spaces, Naci̇ Saldi

Turkish Journal of Mathematics

In stochastic dynamic games, when the number of players is sufficiently large and the interactions between agents depend on empirical state distribution, one way to approximate the original game is to introduce infinitepopulation limit of the problem. In the infinite population limit, a generic agent is faced with a so-called mean-field game. In this paper, we study discrete-time mean-field games with average-cost criteria. Using average cost optimality equation and Kakutani's fixed point theorem, we establish the existence of Nash equilibria for mean-field games under drift and minorization conditions on the dynamics of each agent. Then, we show that the equilibrium …

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The Strong 3-Rainbow Index Of Edge-Amalgamation Of Some Graphs, Zata Yumni Awanis, Anm Salman, Suhadi Wido Saputro, Martin Baca, Andrea Semanicova-Fenovcikova Jan 2020

The Strong 3-Rainbow Index Of Edge-Amalgamation Of Some Graphs, Zata Yumni Awanis, Anm Salman, Suhadi Wido Saputro, Martin Baca, Andrea Semanicova-Fenovcikova

Turkish Journal of Mathematics

Let G be a nontrivial, connected, and edge-colored graph of order n≥? 3, where adjacent edges may be colored the same. Let k be an integer with 2 ≤? k ≤? n. A tree T in G is a rainbow tree if no two edges of T are colored the same. For S ? V (G), the Steiner distance d(S) of S is the minimum size of a tree in G containing S . An edge-coloring of G is called a strong k-rainbow coloring if for every set S of k vertices of G there exists a rainbow tree of …

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Dissipative Canonical Type Differential Operators For First Order, Ruki̇ye Öztürk Mert, Zameddi̇n İsmai̇lov, Pembe İpek Al Jan 2020

Dissipative Canonical Type Differential Operators For First Order, Ruki̇ye Öztürk Mert, Zameddi̇n İsmai̇lov, Pembe İpek Al

Turkish Journal of Mathematics

In this paper, using the Calkin-Gorbachuk method, the general form of all maximally dissipative extensions of the minimal operator generated by the first order linear symmetric canonical type quasi-differential expression in the weighted Hilbert space of vector functions has been found. Also, the spectrum set of these extensions has been investigated.

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Conceptions On Topological Transitivity In Products And Symmetric Products, Anahi Rojas, Franco Barragan, Sergio Macías Jan 2020

Conceptions On Topological Transitivity In Products And Symmetric Products, Anahi Rojas, Franco Barragan, Sergio Macías

Turkish Journal of Mathematics

Having a finite number of topological spaces $X_i$ and functions $f_i : X_i \to X_i$, and considering one of the following classes of functions: exact, transitive, strongly transitive, totally transitive, orbit-transitive, strictly orbittransitive, $\omega$-transitive, mixing, weakly mixing, mild mixing, chaotic, exactly Devaney chaotic, minimal, backward minimal, totally minimal, $TT_{++}$, scattering, Touhey or an $F$ -system, in this paper, we study dynamical behaviors of the systems $(X_i,f_i)$, $(\prod X_i,\prod f_i)$, $(\mathcal{F}_n(\prod X_i),\mathcal{F}_n(\prod f_i))$, and $(\mathcal{F}_n(X_i),\mathcal{F}_n(f_i))$.

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On Connected Tetravalent Normal Edge-Transitive Cayley Graphs Of Non-Abelian Groups Of Order 5p2, Soghra Khazaei, Hesam Sharifi Jan 2020

On Connected Tetravalent Normal Edge-Transitive Cayley Graphs Of Non-Abelian Groups Of Order 5p2, Soghra Khazaei, Hesam Sharifi

Turkish Journal of Mathematics

Our aim in this paper is to investigate graph automorphism and group automorphism determining all connected tetravalent normal edge transitive Cayley graphs on non-Abelian groups of order 5p2 with respect to tetravalent sets and same-order elements, where p is a prime number and its Sylow p-subgroup is cyclic.

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Some Results Of K-Frames And Their Multipliers, Mitra Shamsabadi, Ali Akbar Arefijamaal Jan 2020

Some Results Of K-Frames And Their Multipliers, Mitra Shamsabadi, Ali Akbar Arefijamaal

Turkish Journal of Mathematics

K-frames are strong tools for the reconstruction of elements from range of a bounded linear operator K on a separable Hilbert space H. In this paper, we study some properties of K-frames and introduce the K-frame multipliers. We also focus on representing elements from the range of K by K-frame multipliers.

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A New Method For Obtaining The Inconsistent Elements In A Decision Table Based On Dominance Principle, Yasemen Uçan, Ahmet Topal, Ni̇lgün Güler Bayazit Jan 2020

A New Method For Obtaining The Inconsistent Elements In A Decision Table Based On Dominance Principle, Yasemen Uçan, Ahmet Topal, Ni̇lgün Güler Bayazit

Turkish Journal of Mathematics

In this study,using only the dominance relation,we propose a set defining inconsistent elements in the decision table. Then, we show the accuracy of our proposition with an example. We also express the computational complexity comparisons of the proposed method with general method in terms of the number of set intersection operations and the real number comparison operations.

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Geodesic Motions In So(2,1), İsmet Ayhan Jan 2020

Geodesic Motions In So(2,1), İsmet Ayhan

Turkish Journal of Mathematics

In this study,we have considered the rotational motions of a particle around the origin of the unit 2-sphere $S_2^2$ with constant angular velocity in semi-Euclidean 3-spacewithindextwo $E^3_2$, namely geodesic motions of $SO(2,1)$. Then we have obtained the vector and the matrix representations of the spherical rotations around the origin of a particle on $S_2^2$. Furthermore, we consider some relations between semi-Riemann spaces $SO(2,1)$ and $T_1S_2^2$ such as diffeomorphism and isometry. We have obtained the system of differential equations giving geodesics of Sasaki semi-Riemann manifold $(T_1S_2^2,g^S)$ . Moreover, we consider the stationary motion of a particle on $S_2^2$ corresponding to one …

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Bounds For A New Subclass Of Bi-Univalent Functions Subordinate To The Fibonacci Numbers, Şahsene Altinkaya Jan 2020

Bounds For A New Subclass Of Bi-Univalent Functions Subordinate To The Fibonacci Numbers, Şahsene Altinkaya

Turkish Journal of Mathematics

In this investigation, by using a relation of subordination, we define a new subclass of analytic bi-univalent functions associated with the Fibonacci numbers. Moreover, we survey the bounds of the coefficients for functions in this class.

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Nonnull Curves With Constant Weighted Curvature In Lorentz-Minkowski Plane With Density, Mustafa Altin, Ahmet Kazan, Haci Bayram Karadağ Jan 2020

Nonnull Curves With Constant Weighted Curvature In Lorentz-Minkowski Plane With Density, Mustafa Altin, Ahmet Kazan, Haci Bayram Karadağ

Turkish Journal of Mathematics

In this paper, the parametric expressions of spacelike and timelike curves with constant weighted curvature for some cases of $a$ and $b$ in Lorentz-Minkowski plane with density $e^{ax+by}$ are obtained.

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On Solvability Of Inverse Problem For One Equation Of Fourth Order, Aysel Ramazanova Telman Qizi, Yashar Mehreliyev Topush Oglu Jan 2020

On Solvability Of Inverse Problem For One Equation Of Fourth Order, Aysel Ramazanova Telman Qizi, Yashar Mehreliyev Topush Oglu

Turkish Journal of Mathematics

The work is devoted to study the existence and uniqueness of the classical solution of the inverse boundary value problem of determining the lowest coefficient in one fourth order equation. The original problem is reduced to an equivalent problem. The existence and uniqueness of the integral equation are proved by means of the contraction mappings principle, and we obtained that this solution is unique for a boundary value problem. Further, using these facts, we prove the existence and uniqueness of the classical solution for this problem.

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Nonlinear Variants Of The Generalized Filbert And Lilbert Matrices, Emrah Kiliç, Si̇bel Koparal, Neşe Ömür Jan 2020

Nonlinear Variants Of The Generalized Filbert And Lilbert Matrices, Emrah Kiliç, Si̇bel Koparal, Neşe Ömür

Turkish Journal of Mathematics

In this paper, we present variants of the generalized Filbert and Lilbert matrices by products of the general Fibonacci and Lucas numbers whose indices are in certain nonlinear forms of the indices with certain integer parameters. We derive explicit formulæ for inverse matrix, LU -decomposition and inverse matrices $L^{-1}$ and $U^{-1}$ for all matrices. Generally, we present $q$-versions of these matrices and their related results.

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A Class Of Fredholm Equations And Systems Of Equations Related To The Kontorovich-Lebedev And The Fourier Integral Transforms, Trinh Tuan, Nguyen Thanh Hong Jan 2020

A Class Of Fredholm Equations And Systems Of Equations Related To The Kontorovich-Lebedev And The Fourier Integral Transforms, Trinh Tuan, Nguyen Thanh Hong

Turkish Journal of Mathematics

In this article, we solve in closed form a class of Fredholm integral equations and systems of Fredholm integral equations with nondegenerate kernels by using techniques of convolutions and generalized convolutions related to the Kontorovich-Lebedev, Fourier sine, and Fourier cosine integral transforms.

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Representations And Properties Of A New Family Of $\Omega$-Caputofractional Derivatives, Abdullah Akkurt, Joel Esteban Restrepo, Hüseyi̇n Yildirim Jan 2020

Representations And Properties Of A New Family Of $\Omega$-Caputofractional Derivatives, Abdullah Akkurt, Joel Esteban Restrepo, Hüseyi̇n Yildirim

Turkish Journal of Mathematics

In the most general case of $\omega$-weights, some normed functional spaces $% X_{\omega}^{p}(a,b)( 1\leq p\leq\infty)$, $AC_{\gamma,\omega}^n[a,b]$ and a generalization of the fractional integro-differentiation operator are introduced and analyzed. The boundedness of the $\omega$-weighted fractional operator over $X_{\omega}^{p}(a,b)$ is proved. Some theorems and lemmas on the properties of the invertions of the mentioned operator and several representations of functions from $AC_{\gamma,\omega}^n[a,b]$ are established. A general $\omega$-weighted Caputo fractional derivative of order $\alpha$ is studied over $AC_{\gamma,\omega}^n[a,b]$. Some representations and other properties of this fractional derivative are proved. Some conclusions are presented.

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Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan Jan 2020

Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan

Turkish Journal of Mathematics

In this paper, we investigate the existence of positive solutions for nonlinear multipoint boundary value problems for p-Laplacian dynamic equations on time scales with the delta derivative of the nonlinear term. Sufficient assumptions are obtained for existence of at least twin or arbitrary even positive solutions to some boundary value problems. Our results are achieved by appealing to the fixed point theorems of Avery-Henderson. As an application, an example to demonstrate our results is given.

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The Bochner-Convolution Integral For Generalized Functional-Valued Functions Of Discrete-Time Normal Martingales, Chen Jinshu Jan 2020

The Bochner-Convolution Integral For Generalized Functional-Valued Functions Of Discrete-Time Normal Martingales, Chen Jinshu

Turkish Journal of Mathematics

Let $M$ be a discrete-time normal martingale satisfying some mild conditions, $\mathcal{S}(M)\subset L^2(M)\subset\mathcal{S}^*(M)$ be the Gel'fand triple constructed from the functionals of $M$. As is known, there is no usual multiplication in $\mathcal{S}^*(M)$ since its elements are continuous linear functionals on $\mathcal{S}(M)$. However, by using the Fock transform, one can introduce convolution in $\mathcal{S}^*(M)$, which suggests that one can try to introduce a type of integral of an $\mathcal{S}^*(M)$-valued function with respect to an $\mathcal{S}^*(M)$-valued measure in the sense of convolution. In this paper, we just define such type of an integral. First, we introduce a class of $\mathcal{S}^*(M)$-valued measures …

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Some Uncertainty Inequalities Related To The Multivariate Laguerre Function, Lotfi Kamoun, Rim Selmi Jan 2020

Some Uncertainty Inequalities Related To The Multivariate Laguerre Function, Lotfi Kamoun, Rim Selmi

Turkish Journal of Mathematics

In this paper, an analogous of the Heisenberg's inequality is established and three inequalities that constitute local uncertainty principle for the generalized Fourier-Laguerre transform in several variables are developed.

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Oscillation Criteria For Higher-Order Neutral Type Difference Equations, Turhan Köprübaşi, Zafer Ünal, Yaşar Bolat Jan 2020

Oscillation Criteria For Higher-Order Neutral Type Difference Equations, Turhan Köprübaşi, Zafer Ünal, Yaşar Bolat

Turkish Journal of Mathematics

In this paper, oscillation criteria are obtained for higher-order neutral-type nonlinear delay difference equations of the form% \begin{equation} \Delta (r_{n}(\Delta ^{k-1}(y_{n}+p_{n}y_{\tau _{n}}))+q_{n}f(y_{\sigma _{n}})=0\text{, }n\geq n_{0}\text{,} \tag{0.1} \end{equation}% where $r_{n},p_{n},q_{n}\in \lbrack n_{0},\infty ),$ $r_{n}>0$, $q_{n}>0$; $% 0\leq p_{n}\leq p_{0}0$; $\tau _{\sigma }=\sigma _{\tau }$; $\frac{f(u)}{u}\geq m>0$ for $u\neq 0$. Moreover, we provide some examples to illustrate our main results.

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A Class Of Warped Product Submanifolds Of Kenmotsu Manifolds, Shyamal Kumar Hui, Mica S. Stankovic, Joydeb Roy, Tanumoy Pal Jan 2020

A Class Of Warped Product Submanifolds Of Kenmotsu Manifolds, Shyamal Kumar Hui, Mica S. Stankovic, Joydeb Roy, Tanumoy Pal

Turkish Journal of Mathematics

In 2018 Naghi et al.studied warped product skew CR-submanifold of the form $M=M_1\times_f M_\perp$ of a Kenmotsu manifold $\bar{M}$ (throughout the paper), where $M_1=M_T\times M_\theta$ and $M_T, M_\perp, M_\theta$ represents invariant, antiinvariant, proper slant submanifold of $\bar{M}$. Next, in 2019 Hui et al. studied another class of warped product skew CR-submanifold of the form $M=M_2\times_fM_T$ of $\bar{M}$, where $M_2=M_\perp\times M_\theta$. The present paper deals with the study of a class of warped product submanifold of the form $M=M_3\times_fM_\theta$ of $\bar{M}$, where $M_3=M_T\times M_\perp$ and $M_T, M_\perp, M_\theta$ represents invariant, antiinvariant and proper pointwise slant submanifold of $\bar{M}$ . A characterization …

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Stability In Commutative Rings, Başak Ay Saylam Jan 2020

Stability In Commutative Rings, Başak Ay Saylam

Turkish Journal of Mathematics

Let $R$ be a commutative ring with zero-divisors and $I$ an ideal of $R$. $I$ is said to be ES-stable if $JI=I^2$ for some invertible ideal $J \subseteq I$, and $I$ is said to be a weakly ES-stable ideal if there is an invertible fractional ideal $J$ and an idempotent fractional ideal $E$ of $R$ such that $I=JE$. We prove useful facts for weakly ES-stability and investigate this stability in Noetherian-like settings. Moreover, we discuss a question of A. Mimouni on locally weakly ES-stable rings: is a locally weakly ES-stable domain of finite character weakly ES-stable?

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