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Computational Identities For Extensions Of Some Families Of Special Numbers And Polynomials, İrem Küçükoğlu, Yilmaz Şi̇mşek
Computational Identities For Extensions Of Some Families Of Special Numbers And Polynomials, İrem Küçükoğlu, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
The main purpose of this paper is to obtain computational identities and formulas for a certain class of combinatorial-type numbers and polynomials. By the aid of the generating function technique, we derive a recurrence relation and an infinite series involving the aforementioned class of combinatorial-type numbers. By applying the Riemann integral to the combinatorial-type polynomials with multivariables, we present some integral formulas for these polynomials, including the Bernoulli numbers of the second kind. By the implementation of the $p$-adic integral approach to the combinatorial-type polynomials with multivariables, we also obtain formulas for the Volkenborn integral and the fermionic $p$-adic integral …
Two-Weight Norm Inequalities For Some Fractional Type Operators Related To Schrödinger Operator On Weighted Morrey Spaces, Wanyu Wu, Jiang Zhou
Two-Weight Norm Inequalities For Some Fractional Type Operators Related To Schrödinger Operator On Weighted Morrey Spaces, Wanyu Wu, Jiang Zhou
Turkish Journal of Mathematics
In this paper, we establish the two-weight norm inequalities for fractional maximal functions and fractional integral operators related to Schrödinger differential operator on weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class.
Asymptotic Properties Of Solutions To Second-Order Difference Equations, Janusz Migda
Asymptotic Properties Of Solutions To Second-Order Difference Equations, Janusz Migda
Turkish Journal of Mathematics
In this paper the second-order difference equations of the form \[ \Delta^2 x_n=a_nf(n,x_{\sigma(n)})+b_n \] are considered. We establish sufficient conditions for the existence of solutions with prescribed asymptotic behavior. In particular, we present conditions under which there exists an asymptotically linear solution. Moreover, we study the asymptotic behavior of solutions.
Submanifolds Of Almost Poly-Norden Riemannian Manifolds, Selcen Yüksel Perktaş
Submanifolds Of Almost Poly-Norden Riemannian Manifolds, Selcen Yüksel Perktaş
Turkish Journal of Mathematics
Our aim in the present paper is to initiate the study of submanifolds in an almost poly-Norden Riemannian manifold, which is a new type of manifold first introduced by Şahin [17]. We give fundamental properties of submanifolds equipped with induced structures provided by almost poly-Norden Riemannian structures and find some conditions for such submanifolds to be totally geodesics. We introduce some subclasses of submanifolds in almost poly-Norden Riemannian manifolds such as invariant and antiinvariant submanifolds. We investigate conditions for a hypersurface of almost poly-Norden Riemannian manifolds to be invariant and totally geodesic, respectively, by using the components of the structure …
Nonabelian Cocycles And The Spectrum Of A Symmetric Monoidal Category, Antonio M. Cegarra
Nonabelian Cocycles And The Spectrum Of A Symmetric Monoidal Category, Antonio M. Cegarra
Turkish Journal of Mathematics
We present an Eilenberg-MacLane-type description for the first, second and third spaces of the spectrum defined by a symmetric monoidal category.
Galerkin-Like Method For Solving Linear Functional Differential Equations Underinitial Conditions, Şuayi̇p Yüzbaşi, Murat Karaçayir
Galerkin-Like Method For Solving Linear Functional Differential Equations Underinitial Conditions, Şuayi̇p Yüzbaşi, Murat Karaçayir
Turkish Journal of Mathematics
In this paper, we present a weighted residual Galerkin method to solve linear functional differential equations. We consider the problem with variable coefficients under initial conditions. Assuming the exact solution of the problem has a Taylor series expansion convergent in the relevant domain, we seek a solution of the given problem in the form of a polynomial having degree $N$ of our choice. Substituting this polynomial with unknown coefficients in the given equation yields an expression linear in these coefficients. We then proceed as in the weighted residual method and take inner product of this expression with monomials up to …
Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc, Sarbeswar Barik
Coefficient Estimation Of A Certain Subclass Of Bi-Close-To-Convex Functions Analytic In The Exterior Of The Unit Disc, Sarbeswar Barik
Turkish Journal of Mathematics
In this paper, we introduce two new subclasses of biunivalent functions analytic in the exterior of the unit disc. The bounds obtained for the $zero^{th}$, first and second coefficient improves upon earlier known results. The results are obtained by refining the well-known estimates for the initial coefficients of the Carth$\acute{e}$odory functions.
Weighted Composition Operators From The Bloch Space To Nth Weighted-Typespaces, Ebrahim Abbasi, Songxiao Li, Hamid Vaezi
Weighted Composition Operators From The Bloch Space To Nth Weighted-Typespaces, Ebrahim Abbasi, Songxiao Li, Hamid Vaezi
Turkish Journal of Mathematics
In this work, we characterize the boundedness of weighted composition operators from the Bloch space and the little Bloch space to $n$th weighted-type spaces. Some estimates for the essential norm of these operators are also given. As a corollary, we obtain some characterizations for the compactness of weighted composition operators from the Bloch space and the little Bloch space to $n$th weighted-type spaces.
The $2$-Adic And $3$-Adic Valuation Of The Tripell Sequence And An Application, Jhon Jairo Bravo, Maribel Díaz, José Luis Ramírez
The $2$-Adic And $3$-Adic Valuation Of The Tripell Sequence And An Application, Jhon Jairo Bravo, Maribel Díaz, José Luis Ramírez
Turkish Journal of Mathematics
Let $(T_n)_{n\geq 0}$ denote the Tripell sequence, defined by the linear recurrence $T_n=2T_{n-1} + T_{n-2}+T_{n-3}$ for $n\geq 3$ with $T_0=0$, $T_{1}=1$ and $T_2=2$ as initial conditions. In this paper, we study the $2$-adic and $3$-adic valuation of the Tripell sequence and, as an application, we determine all Tripell numbers which are factorials.
Locally $D_\Delta$-Connected And Locally $D_\Delta$-Compact Spaces, Harshit Mathur, Davinder Singh
Locally $D_\Delta$-Connected And Locally $D_\Delta$-Compact Spaces, Harshit Mathur, Davinder Singh
Turkish Journal of Mathematics
The local analogues of the notions of $d_\delta$-connectedness and $D_\delta$-compactness of a topological space are introduced, and are named respectively, locally $d_\delta$-connectedness and locally $D_\delta$-compactness. Several properties including characterization of the concepts are discussed.
Geometric Properties Of Partial Sums Of Generalized Koebe Function, Erhan Deni̇z, Erkan Yalçin
Geometric Properties Of Partial Sums Of Generalized Koebe Function, Erhan Deni̇z, Erkan Yalçin
Turkish Journal of Mathematics
The aim of the present paper is to investigate the starlikeness, convexity, and close-to-convexity of some partial sums of the generalized Koebe function. Furthermore, we give some special results related with special cases of $c$ constant. The results, which are presented in this paper, would generalize those in related works of several earlier authors.
General Coefficient Estimates For Bi-Univalent Functions: A New Approach, Oqlah Alrefai, Mohammed Ali
General Coefficient Estimates For Bi-Univalent Functions: A New Approach, Oqlah Alrefai, Mohammed Ali
Turkish Journal of Mathematics
We prove for univalent functions $f(z)=z+\sum_{k=n}^{\infty}a_k z^k;(n\geq 2)$ in the unit disk $\mathbb{U}=\{z:\; z
A Reduced Computational Matrix Approach With Convergence Estimation For Solving Model Differential Equations Involving Specific Nonlinearities Of Quartic Type, Ömür Kivanç Kürkçü
A Reduced Computational Matrix Approach With Convergence Estimation For Solving Model Differential Equations Involving Specific Nonlinearities Of Quartic Type, Ömür Kivanç Kürkçü
Turkish Journal of Mathematics
This study aims to efficiently solve model differential equations involving specific nonlinearities of quartic type by proposing a reduced computational matrix approach based on the generalized Mott polynomial. This method presents a reduced matrix expansion of the generalized Mott polynomial with the parameter-$\alpha$, matrix equations, and Chebyshev--Lobatto collocation points. The simplicity of the method provides fast computation while eliminating an algebraic system of nonlinear equations, which arises from the matrix equation. The method also scrutinizes the consistency of the solutions due to the parameter-$\alpha$. The oscillatory behavior of the obtained solutions on long time intervals is simulated via a coupled …
Conformally Flat Willmore Spacelike Hypersurfaces In $\Mathbb{R}^{N+1}_1$, Zonggang Deng, Tongzhu Li
Conformally Flat Willmore Spacelike Hypersurfaces In $\Mathbb{R}^{N+1}_1$, Zonggang Deng, Tongzhu Li
Turkish Journal of Mathematics
In this paper, we give the equation satisfied by umbilics-free Willmore spacelike hypersurfaces using the conformal invariants in Lorentzian space forms. At the same time, we give the equation satisfied by hyperelastic spacelike curves in $2$-dimensional Lorentzian space forms and classify the closed hyperelastic spacelike curves. Finally conformally flat Willmore spacelike hypersurfaces are classified in terms of the hyperelastic spacelike curves in $2$-dimensional Lorentzian space forms.
Vector Fields And Planes In $\Mathbb{E}^4$ Which Play The Role Of Darboux Vector, Mustafa Düldül
Vector Fields And Planes In $\Mathbb{E}^4$ Which Play The Role Of Darboux Vector, Mustafa Düldül
Turkish Journal of Mathematics
In this paper, we define some new vector fields along a space curve with nonvanishing curvatures in Euclidean 4-space. By using these vector fields we determine some new planes, curves, and ruled hypersurfaces. We show that the determined new planes play the role of the Darboux vector. We also show that, contrary to their definitions, osculating curves of the first kind and rectifying curves in Euclidean 4-space can be considered as space curves whose position vectors always lie in a two-dimensional subspace. Furthermore, we construct developable and nondevelopable ruled hypersurfaces associated with the new vector fields in which the base …
Direct And Inverse Approximation Theorems In The Weighted Orlicz-Type Spaces With A Variable Exponent, Fahreddi̇n Abdullayev, Stanislav Chaichenko, Meerim Imash Kyzy, Andrii Shidlich
Direct And Inverse Approximation Theorems In The Weighted Orlicz-Type Spaces With A Variable Exponent, Fahreddi̇n Abdullayev, Stanislav Chaichenko, Meerim Imash Kyzy, Andrii Shidlich
Turkish Journal of Mathematics
In weighted Orlicz-type spaces ${\mathcal S}_{_{\scriptstyle \mathbf p,\,\mu}}$ with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of smoothness of fractional order. It is shown that the constant obtained in the inverse approximation theorem is the best in a certain sense. Some applications of the results are also proposed. In particular, the constructive characteristics of functional classes defined by such moduli of smoothness are given. Equivalence between moduli of smoothness and certain Peetre $K$-functionals is shown in the spaces ${\mathcal S}_{_{\scriptstyle \mathbf p,\,\mu}}$.
Evaluation Of Sums Of Products Of Gaussian $Q$-Binomial Coefficients With Rational Weight Functions, Talha Arikan, Emrah Kiliç, Helmut Prodinger
Evaluation Of Sums Of Products Of Gaussian $Q$-Binomial Coefficients With Rational Weight Functions, Talha Arikan, Emrah Kiliç, Helmut Prodinger
Turkish Journal of Mathematics
Generalizing earlier results, sums over the products of the Gaussian $q$-binomial coefficients are computed. Some applications of the results for special choices of $q$ are emphasized. The results are obtained by the elementary technique of partial fraction decomposition.
A Generalization Of The Minkowski Distance And New Definitions Of The Central Conics, Harun Bariş Çolakoğlu
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.
Continuous Dependence Of Solutions For Damped Improved Boussinesq Equation, Sema Bayraktar, Şevket Gür
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.
Coefficient Estimates For The Class Of Quasi Q-Convex Functions, Osman Altintaş, Seher Meli̇ke Aydoğan
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.
Approximation By Matrix Transforms In Weighted Orlicz Spaces, Sadulla Jafarov
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.
On Extensions Of Two Results Due To Ramanujan, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris
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.
The Formulization Of The Intrinsic Metric On The Added Sierpinski Triangle By Using The Code Representations, Aslihan İkli̇m Şen, Mustafa Saltan
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 …
Prolongations Of Isometric Actions To Vector Bundles, Hülya Kadioğlu
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 $\mathbb{E}/\tilde{G}$.
Faber-Laurent Series In Variable Smirnov Classes, Dani̇yal İsrafi̇lzade, Eli̇fe Gürsel
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.
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
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.
Regular Sequences In The Subrings Of C(X), Fariborz Azarpanah, Delavar Esmaeilvandi
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 …
Discrete-Time Average-Cost Mean-Field Games On Polish Spaces, Naci̇ Saldi
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 …
The Strong 3-Rainbow Index Of Edge-Amalgamation Of Some Graphs, Zata Yumni Awanis, Anm Salman, Suhadi Wido Saputro, Martin Baca, Andrea Semanicova-Fenovcikova
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 …