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Evaluation Of Sums Involving Products Of Gaussian $Q$-Binomial Coefficients With Applications To Fibonomial Sums, Emrah Kiliç, Helmut Prodinger
Evaluation Of Sums Involving Products Of Gaussian $Q$-Binomial Coefficients With Applications To Fibonomial Sums, Emrah Kiliç, Helmut Prodinger
Turkish Journal of Mathematics
Sums of products of two Gaussian $q$-binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting applications of these results to certain generalized Fibonomial and Lucanomial sums are provided.
Numerical Method For Solving Linear Stochasticito-Volterra Integral Equations Driven By Fractional Brownian Motion Using Hat Functions, Bentol Hoda Hashemi, Morteza Khodabin, Khosrow Maleknejad
Numerical Method For Solving Linear Stochasticito-Volterra Integral Equations Driven By Fractional Brownian Motion Using Hat Functions, Bentol Hoda Hashemi, Morteza Khodabin, Khosrow Maleknejad
Turkish Journal of Mathematics
In this paper, we present a numerical method to approximate the solution of linear stochastic Ito-Volterra integral equations driven by fractional Brownian motion with Hurst parameter $ H \in (0,1)$ based on a stochastic operational matrix of integration for generalized hat basis functions. We obtain a linear system of algebraic equations with a lower triangular coefficients matrix from the linear stochastic integral equation, and by solving it we get an approximation solution with accuracy of order $ \emph{O}(h^2)$. This numerical method shows that results are more accurate than the block pulse functions method where the rate of convergence is $ …
A Two-Obstacle Problem With Variable Exponent And Measure Data, Hongtao Li, Xiaojuan Chai
A Two-Obstacle Problem With Variable Exponent And Measure Data, Hongtao Li, Xiaojuan Chai
Turkish Journal of Mathematics
We consider a two-obstacle problem with measure data. For measures that do not charge sets of zero $p(\cdot)$-capacity, we obtain the existence and uniqueness of the solution. On the other hand, for the measure concentrated on a set with zero $p(\cdot)$-capacity, we prove a nonexistence result in the sense that when one looks for solutions via approximation, one cannot find a reasonable solution; see Theorem 2.3 and Remark 2.1 below.
Simultaneous Strong Proximinality In Banach Spaces, Sahil Gupta, Tulsi Dass Narang
Simultaneous Strong Proximinality In Banach Spaces, Sahil Gupta, Tulsi Dass Narang
Turkish Journal of Mathematics
Several researchers have discussed the problem of strong proximinality in Banach spaces. In this paper, we generalize the notion of strong proximinality and define simultaneous strong proximinality. It is proved that if $W$ is a simultaneously approximatively compact subset of a Banach space $X$ then $W$ is simultaneously strongly proximinal and the converse holds if the set of all best simultaneous approximations to every bounded subset $S$ of $X$ from $W$ is compact. We show that simultaneously strongly Chebyshev sets are precisely the sets that are simultaneously strongly proximinal and simultaneously Chebyshev. It is also proved that if $F$ and …
Asymptotic For A Second-Order Evolution Equation With Convex Potential Andvanishing Damping Term, Ramzi May
Asymptotic For A Second-Order Evolution Equation With Convex Potential Andvanishing Damping Term, Ramzi May
Turkish Journal of Mathematics
In this short note, we recover by a different method the new result due to Attouch, Chbani, Peyrouqet, and Redont concerning the weak convergence as $t\rightarrow+\infty$ of solutions $x(t)$ to the second-order differential equation $x^{\prime\prime}(t)+\frac{K}{t}x^{\prime}(t)+\nabla\Phi(x(t))=0,$ where $K>3$ and $\Phi$\ is a smooth convex function defined on a Hilbert space $\mathcal{H}.$ Moreover, we improve their result on the rate of convergence of $\Phi(x(t))-\min\Phi.$
Choosing The Relaxation Parameter In Sequential Block-Iterativemethods For Linear Systems, Touraj Nikazad, Shsghayegh Heidarzade
Choosing The Relaxation Parameter In Sequential Block-Iterativemethods For Linear Systems, Touraj Nikazad, Shsghayegh Heidarzade
Turkish Journal of Mathematics
In this paper we introduce two strategies for picking relaxation parameters to control the semiconvergence behavior of a sequential block-iterative method. A convergence analysis is presented. We also demonstrate the performance of our strategies by examples taken from tomographic imaging.
$Cc$-Normal Topological Spaces, Lutfi Kalantan, Manal Alhomieyed
$Cc$-Normal Topological Spaces, Lutfi Kalantan, Manal Alhomieyed
Turkish Journal of Mathematics
A topological space $X$ is called \it $CC$-normal \rm if there exist a normal space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f_{ _A}:A\longrightarrow f(A)$ is a homeomorphism for each countably compact subspace $A\subseteq X$. We will investigate this property and produce some examples to illustrate the relation between $CC$-normality and other weaker kinds of normality.
When Zero-Divisor Graphs Are Divisor Graphs, Emad Abu Osba, Osama Alkam
When Zero-Divisor Graphs Are Divisor Graphs, Emad Abu Osba, Osama Alkam
Turkish Journal of Mathematics
Let $R$ be a finite commutative principal ideal ring with unity. In this article, we prove that the zero-divisor graph $\Gamma(R)$ is a divisor graph if and only if $R$ is a local ring or it is a product of two local rings with at least one of them having diameter less than $2$. We also prove that $\Gamma(R)$ is a divisor graph if and only if $\Gamma(R[x])$ is a divisor graph if and only if $\Gamma(R[[x]])$ is a divisor graph.
A Goal Programming Approach For Solving The Random Interval Linear Programming Problem, Ziba Arjmandzadeh, Mohammadreza Safi
A Goal Programming Approach For Solving The Random Interval Linear Programming Problem, Ziba Arjmandzadeh, Mohammadreza Safi
Turkish Journal of Mathematics
This paper presents a goal programming model for solving linear programming problems involving random interval coefficients. In this model, a random interval with known characters is considered as the aspiration level (target) of the objective function. The original problem involving random interval parameters is transformed into a biobjective equivalent problem using the proposed model. Defining an auxiliary variable, an approach for solving the biobjective problem is presented. Two numerical examples are carried out to show the efficiency of the proposed model.
Convergence Analysis Of Parabolic Basis Functions For Solving Systems Of Linear And Nonlinear Fredholm Integral Equations, Yousef Jafarzadeh, Bagher Keramati
Convergence Analysis Of Parabolic Basis Functions For Solving Systems Of Linear And Nonlinear Fredholm Integral Equations, Yousef Jafarzadeh, Bagher Keramati
Turkish Journal of Mathematics
In this paper, a computational method based on a hybrid of parabolic and block-pulse functions is proposed to solve a system of linear and special nonlinear Fredholm integral equations of the second kind. The convergence and error bound are analyzed. Numerical examples are given to illustrate the efficiency of the method.
Arithmetic Properties Of $\Ell$-Regular Overpartition Pairs, Megadahalli Siddanaika Mahadeva Naika, Chandrappa Shivashankar
Arithmetic Properties Of $\Ell$-Regular Overpartition Pairs, Megadahalli Siddanaika Mahadeva Naika, Chandrappa Shivashankar
Turkish Journal of Mathematics
In this paper, we investigate the arithmetic properties of $\ell$-regular overpartition pairs. Let $\overline{B}_{\ell}(n)$ denote the number of $\ell$-regular overpartition pairs of $n$. We will prove the number of Ramanujan-like congruences and infinite families of congruences modulo 3, 8, 16, 36, 48, 96 for $\overline{B}_3(n)$ and modulo 3, 16, 64, 96 for $\overline{B}_4(n)$. For example, we find that for all nonnegative integers $\alpha$ and $n$, $\overline{B}_{3}(3^{\alpha}(3n+2))\equiv 0\pmod{3}$, $\overline{B}_{3}(3^{\alpha}(6n+4))\equiv 0\pmod{3}$, and $\overline{B}_{4}(8n+7)\equiv 0\pmod{64}$.
Product Of Arbitrary Fibonacci Numbers With Distance 1 To Fibonomial Coefficient, Nuretti̇n Irmak
Product Of Arbitrary Fibonacci Numbers With Distance 1 To Fibonomial Coefficient, Nuretti̇n Irmak
Turkish Journal of Mathematics
In this paper, we solve completely the Diophantine equation \begin{gather} F_{n_{1}}F_{n_{2}}\ldots F_{n_{k}}\pm 1={m\brack t}_{F} \end{gather} for $t=1$ and $t=2$ where $2$ < $n_{1}$ < $n_{2}$ < $\ldots$ < $n_{k}$ positive integers and ${m\brack t}_{F}$ is the Fibonomial coefficient.
Penalty-Free Method For Nonsmooth Constrained Optimization Via Radial Basis Functions, Fardin Rahmanpour, Mohammad Mehdi Hosseini, Farid Mohammad Maalek Ghaini
Penalty-Free Method For Nonsmooth Constrained Optimization Via Radial Basis Functions, Fardin Rahmanpour, Mohammad Mehdi Hosseini, Farid Mohammad Maalek Ghaini
Turkish Journal of Mathematics
We consider a general class of nonlinear constrained optimization problems, where derivatives of the objective function and constraints are unavailable. This property of problems can often impede the performance of optimization algorithms. Most algorithms usually determine a quasi-Newton direction and then use line search techniques. We propose a smoothing algorithm without the need to use a penalty function. A new algorithm is developed to modify the trust region and to handle the constraints based on radial basis functions (RBFs). The value of the objective function is reduced according to the relation of the predicted reduction of constraint violation achieved by …
Generalized $\Ast$-Lie Ideal Of $\Ast$-Prime Ring, Seli̇n Türkmen, Neşet Aydin
Generalized $\Ast$-Lie Ideal Of $\Ast$-Prime Ring, Seli̇n Türkmen, Neşet Aydin
Turkish Journal of Mathematics
Let $R$ be a $\ast$-prime ring with characteristic not $2,$ $\sigma, \tau:R\rightarrow R$ be two automorphisms, $U$ be a nonzero $\ast$-$\left( \sigma,\tau\right) $-Lie ideal of $R$ such that $\tau~$commutes with $\ast$, and $a,b$ be in $R.$ $\left( i\right) $ If $a\in S_{\ast}\left( R\right) $ and $\left[ U,a\right] =0$, then $a\in Z\left( R\right) $ or $U\subset Z\left( R\right) .$ $\left( ii\right) $ If $a\in S_{\ast}\left( R\right) $ and $\left[ U,a\right] _{\sigma,\tau}\subset$ $C_{\sigma,\tau}$, then $a\in Z\left( R\right) ~$or$~U\subset Z\left( R\right) .$ $\left( iii\right) $ If $U\not \subset Z\left( R\right) $ and $U\not \subset C_{\sigma,\tau}$, then there exists a nonzero $\ast$-ideal $M$ of …
Graph-Directed Fractal Interpolation Functions, Ali̇ Deni̇z, Yunus Özdemi̇r
Graph-Directed Fractal Interpolation Functions, Ali̇ Deni̇z, Yunus Özdemi̇r
Turkish Journal of Mathematics
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system, which is called a fractal interpolation function. We generalize the notion of the fractal interpolation function to the graph-directed case and prove that for a finite number of data sets there exist interpolation functions each of which interpolates a corresponding data set in $\mathbb{R}^2$ such that the graphs of the interpolation functions are attractors of a graph-directed iterated function system.
Coefficient Bounds For A New Subclass Of Analytic Bi-Close-To-Convex Functions By Making Use Of Faber Polynomial Expansion, Fethi̇ye Müge Sakar, Hatun Özlem Güney
Coefficient Bounds For A New Subclass Of Analytic Bi-Close-To-Convex Functions By Making Use Of Faber Polynomial Expansion, Fethi̇ye Müge Sakar, Hatun Özlem Güney
Turkish Journal of Mathematics
Recently, in the literature, we can see quite a few papers about general coefficient bounds for subclasses of bi-univalent functions. However, we can find just a few papers about general coefficient estimates for subclasses of bi-close-to-convex functions. In the present study, we give and look into a new subclass of analytic and bi-close-to-convex functions in the open unit disk. Making use of the Faber series, we have an upper bound for the general coefficient of functions in this class. We also demonstrate the invisible behavior of the beginning coefficients of a special subclass of bi-close-to-convex functions.
On The Stochastic Decomposition Property Of Single Server Retrialqueuing Systems, Nawel Arrar, Natalia Djellab, Jean-Bernard Baillon
On The Stochastic Decomposition Property Of Single Server Retrialqueuing Systems, Nawel Arrar, Natalia Djellab, Jean-Bernard Baillon
Turkish Journal of Mathematics
The study of retrial queuing systems presents great analytical difficulties. Detailed results are available for some models, whereas for other models the obtained results revealed poor information and are cumbersome (they contain Laplace transforms, integral expressions, etc.). Therefore, in practice, they present limited performance. Often, to overcome this difficulty, we use an approach based on the stochastic decomposition property that can be possessed by the model. It offers the advantages of simplification of solving complex models. This paper deals with the stochastic decomposition property of an M$^{X}$/G/1 retrial queue with impatient customers and exponential retrial times and of an M/G/1 …
Singular Dirac Systems In The Sobolev Space, Eki̇n Uğurlu
Singular Dirac Systems In The Sobolev Space, Eki̇n Uğurlu
Turkish Journal of Mathematics
In this paper we construct Weyl's theory for the singular left-definite Dirac systems. In particular, we prove that there exists at least one solution of the system of equations that lies in the Sobolev space. Moreover, we describe the behavior of the solution belonging to the Sobolev space around the singular point.
On Golden Semisymmetric Metric $F$-Connections, Aydin Gezer, Çağri Karaman
On Golden Semisymmetric Metric $F$-Connections, Aydin Gezer, Çağri Karaman
Turkish Journal of Mathematics
In this paper, we construct a golden semisymmetric metric $F$-connection on a locally decomposable golden Riemannian manifold and investigate some properties of its curvature, conharmonic curvature, Weyl projective curvature, and torsion tensors. Moreover, we define the transposed connection of this connection and study its curvature properties.
Cardinal Hermite Interpolant Multiscaling Functions For Solving A Parabolic Inverse Problem, Elmira Ashpazzadeh, Mehrdad Lakestani, Mohsen Razzaghi
Cardinal Hermite Interpolant Multiscaling Functions For Solving A Parabolic Inverse Problem, Elmira Ashpazzadeh, Mehrdad Lakestani, Mohsen Razzaghi
Turkish Journal of Mathematics
An effective method based upon cardinal Hermite interpolant multiscaling functions is proposed for the solution of the one-dimensional parabolic partial differential equation with given initial condition and known boundary conditions and subject to overspecification at a point in the spatial domain. The properties of multiscaling functions are first presented. These properties together with a collocation method are then utilized to reduce the parabolic inverse problem to the solution of algebraic equations. The scheme described is efficient. The numerical results obtained using the present algorithms for test problems show that this method can solve the model effectively.
Finite Volume Approximation Of The Relativistic Burgers Equation On A Schwarzschild-(Anti-)De Sitter Spacetime, Tuba Ceylan, Baver Okutmuştur
Finite Volume Approximation Of The Relativistic Burgers Equation On A Schwarzschild-(Anti-)De Sitter Spacetime, Tuba Ceylan, Baver Okutmuştur
Turkish Journal of Mathematics
The relativistic versions of Burgers equations on the Schwarzschild, FLRW, and de Sitter backgrounds have recently been derived and analyzed numerically via finite volume approximation based on the concerned models. In this work, we derive the relativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime and introduce a second-order Godunov-type finite volume scheme for the approximation of discontinuous solutions to the model of interest. The effect of the cosmological constant is also taken into account both theoretically and numerically. The efficiency of the method for solutions containing shock and rarefaction waves are presented by several numerical experiments.
Almost Contact Metric Structures Induced By $G_2$ Structures, Nüli̇fer Özdemi̇r, Mehmet Solgun, Şi̇ri̇n Aktay
Almost Contact Metric Structures Induced By $G_2$ Structures, Nüli̇fer Özdemi̇r, Mehmet Solgun, Şi̇ri̇n Aktay
Turkish Journal of Mathematics
We study almost contact metric structures induced by 2-fold vector cross products on manifolds with $G_2$ structures. We get some results on possible classes of almost contact metric structures. Finally, we give examples.
On $\Lambda$-Perfect Maps, Mehrdad Namdari, Mohammad Ali Siavoshi
On $\Lambda$-Perfect Maps, Mehrdad Namdari, Mohammad Ali Siavoshi
Turkish Journal of Mathematics
$\lambda$-Perfect maps, a generalization of perfect maps (i.e. continuous closed maps with compact fibers) are presented. Using $P_\lambda$-spaces and the concept of $\lambda$-compactness some classical results regarding $\lambda$-perfect maps will be extended. In particular, we show that if the composition $fg$ is a $\lambda$-perfect map where $f,g$ are continuous maps with $fg$ well-defined, then $f,g$ are $\alpha$-perfect and $\beta$-perfect, respectively, on appropriate spaces, where $\alpha, \beta\leq\lambda$.
Terminal Value Problem For Causal Differential Equations With A Caputofractional Derivative, Coşkun Yakar, Mehmet Arslan
Terminal Value Problem For Causal Differential Equations With A Caputofractional Derivative, Coşkun Yakar, Mehmet Arslan
Turkish Journal of Mathematics
In this paper, we have given new definitions and obtained the unique solution of a fractional causal terminal value problem by combining the technique of generalized quasilinearization in the sense of upper and lower solutions.
Some Theorems For A New Type Of Multivalued Contractivemaps On Metric Space, Gonca Durmaz
Some Theorems For A New Type Of Multivalued Contractivemaps On Metric Space, Gonca Durmaz
Turkish Journal of Mathematics
In this paper, taking into account the function $\theta $, we introduce a new type of contraction for multivalued maps on metric space. This new concept includes many known contractions in the literature. We then present some fixed point results for closed and bounded set valued maps on complete metric space. Finally, we provide an example to show the significance of the investigation of this paper.
Permutation Groups With Cyclic-Block Property And $Mnfc$-Groups, Ali̇ Osman Asar
Permutation Groups With Cyclic-Block Property And $Mnfc$-Groups, Ali̇ Osman Asar
Turkish Journal of Mathematics
This work continues the investigation of perfect locally finite minimal non-$FC$-groups in totally imprimitive permutation $p$-groups. At present, the class of totally imprimitive permutation $p$-groups satisfying the cyclic-block property is known to be the only class of $p$-groups having common properties with a hypothetical minimal non-$FC$-group, because a totally imprimitive permutation $p$-group satisfying the cyclic-block property cannot be generated by a subset of finite exponent and every non-$FC$-subgroup of it is transitive, which are the properties satisfied by a minimal non-$FC$-group. Here a sufficient condition is given for the nonexistence of minimal non-$FC$-groups in this class of permutation groups. In …
Positive Periodic Solutions To Impulsive Delay Differentialequations, Naima Daoudi-Merzagui, Fatima Dib
Positive Periodic Solutions To Impulsive Delay Differentialequations, Naima Daoudi-Merzagui, Fatima Dib
Turkish Journal of Mathematics
In this paper we discuss the existence of positive periodic solutions for nonautonomous second order delay differential equations with singular nonlinearities in the presence of impulsive effects. Simple sufficient conditions are provided that enable us to obtain positive periodic solutions. Our approach is based on a variational method.
Unicorn Metrics With Almost Vanishing ${\Bf H}$- And ${\Bf \Xi}$-Curvatures, Akbar Tayebi, Tayebeh Tabatabaeifar
Unicorn Metrics With Almost Vanishing ${\Bf H}$- And ${\Bf \Xi}$-Curvatures, Akbar Tayebi, Tayebeh Tabatabaeifar
Turkish Journal of Mathematics
In this paper, we consider a class of almost regular $(\alpha, \beta)$-metrics constructed by Shen called unicorn metrics. First, we prove that every unicorn metric with almost vanishing ${\bf H}$-curvature is a Berwald metric. Then we show that every unicorn metric with almost vanishing $\Xi$-curvature reduces to a Berwald metric.
On The 3-Dimensional Hopf Bifurcation Via Averaging Theory Of Third Order, Elouahma Bendib, Sabrina Badi, Ammar Makhlouf
On The 3-Dimensional Hopf Bifurcation Via Averaging Theory Of Third Order, Elouahma Bendib, Sabrina Badi, Ammar Makhlouf
Turkish Journal of Mathematics
We apply the averaging theory of third order to polynomial quadratic vector fields in $\mathbb{R}^3$ to study the Hopf bifurcation occurring in that polynomial. Our main result shows that at most $10$ limit cycles can bifurcate from a singular point having eigenvalues of the form $\pm bi$ and $0$. We provide an example of a quadratic polynomial differential system for which exactly $10$ limit cycles bifurcate from a such singular point.
Subspace Condition For Bernstein's Lethargy Theorem, Asuman Güven Aksoy, Monairah Al-Ansari, Caleb Case, Qidi Peng
Subspace Condition For Bernstein's Lethargy Theorem, Asuman Güven Aksoy, Monairah Al-Ansari, Caleb Case, Qidi Peng
Turkish Journal of Mathematics
In this paper, we consider a condition on subspaces in order to improve bounds given in Bernstein's lethargy theorem for Banach spaces. Let $d_1 \geq d_2 \geq \dots d_n \geq \dots > 0$ be an infinite sequence of numbers converging to $0$, and let $Y_1 \subset Y_2 \subset \dots\subset Y_n \subset \dots \subset X$ be a sequence of closed nested subspaces in a Banach space $X$ with the property that $\overline{Y}_{n}\subset Y_{n+1}$ for all $n\ge1$. We prove that for any $c ın (0,1]$ there exists an element $x_c ın X$ such that$$ c d_n \leq \rho(x_c, Y_n) \leq \min (4, \tilde{a}) …