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An Exponential Equation Involving $K$-Fibonacci Numbers, Alioune Gueye, Salah Eddine Rihane, Alain Togbe
An Exponential Equation Involving $K$-Fibonacci Numbers, Alioune Gueye, Salah Eddine Rihane, Alain Togbe
Turkish Journal of Mathematics
For $k\geq 2$, consider the $k$-Fibonacci sequence $(F_n^{(k)})_{n\geq 2-k}$ having initial conditions $0, \ldots, 0, 1$ ($k$ terms) and each term afterwards is the sum of the preceding $k$ terms. Some well-known sequences are special cases of this generalization. The Fibonacci sequence is a special case of $(F_n^{(k)})_{n\geq 2-k}$ with $k=2$ and Tribonacci sequence is $(F_n^{(k)})_{n\geq 2-k}$ with $k=3$. In this paper, we use Baker's method to show that 4, 16, 64, 208, 976, and 1936 are all $k$-Fibonacci numbers of the form $(3^a\pm 1)(3^b\pm 1)$, where $a$ and $b$ are nonnegative integers.
Scattering And Characteristic Functions Of A Dissipative Operator Generated By A System Of Equations, Elgi̇z Bayram, Kenan Taş, Eki̇n Uğurlu
Scattering And Characteristic Functions Of A Dissipative Operator Generated By A System Of Equations, Elgi̇z Bayram, Kenan Taş, Eki̇n Uğurlu
Turkish Journal of Mathematics
In this paper, we consider a system of first-order equations with the same eigenvalue parameter together with dissipative boundary conditions. Applying Lax-Phillips scattering theory and Sz.-Nagy-Foiaş model operator theory we prove a completeness theorem.
On The Extension Of Hermite-Hadamard Type Inequalities For Co-Ordinated Convex Mappings, Mehmet Zeki̇ Sarikaya, Di̇lşatnur Kiliçer
On The Extension Of Hermite-Hadamard Type Inequalities For Co-Ordinated Convex Mappings, Mehmet Zeki̇ Sarikaya, Di̇lşatnur Kiliçer
Turkish Journal of Mathematics
In this paper, we obtain an important inequalities for coordinated convex functions and as a result of these inequalities we give the extension of Hermite-Hadamard type inequalities for Riemann-Liouville fractional integral and logarithmic integral. The inequalities obtained in this study provide generalizations of some result given in earlier works.
Cameron-Storvick Theorem Associated With Gaussian Paths On Function Space, Jae Gil Choi
Cameron-Storvick Theorem Associated With Gaussian Paths On Function Space, Jae Gil Choi
Turkish Journal of Mathematics
The purpose of this paper is to provide a more general Cameron-Storvick theorem for the generalized analytic Feynman integral associated with Gaussian process $\mathcal Z_k$ on a very general Wiener space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ can be considered as the set of all continuous sample paths of the generalized Brownian motion process determined by continuous functions $a(t)$ and $b(t)$ on $[0,T]$. As an interesting application, we apply this theorem to evaluate the generalized analytic Feynman integral of certain monomials in terms of Paley-Wiener-Zygmund stochastic integrals.
A Classification Of 1-Well-Covered Graphs, Zaki̇r Deni̇z
A Classification Of 1-Well-Covered Graphs, Zaki̇r Deni̇z
Turkish Journal of Mathematics
A graph is well-covered if all its maximal independent sets have the same size. If a graph is well-covered and remains well-covered upon removal of any vertex, then it is called 1-well-covered graph. It is well-known that $[\frac{n}{2}]+1\leq \alpha(G) + \mu(G) \leq n$ for any graph $G$ with $n$ vertices where $\alpha(G)$ and $\mu(G)$ are the independence and matching numbers of $G$, respectively. A graph $G$ satisfying $\alpha(G) + \mu(G) = n$ is known as König-Egervary graph, and such graphs are characterized by Levit and Mandrescu [14] under the assumption that $G$ is 1-well-covered. In this paper, we investigate connected …
Recent Developments In $\Delta$-Casorati Curvature Invariants, Bang-Yen Chen
Recent Developments In $\Delta$-Casorati Curvature Invariants, Bang-Yen Chen
Turkish Journal of Mathematics
The theory of $\delta$-invariants, initiated by the author in the early 1990s, is a challenging topic in modern differential geometry, having a lot of applications. In the spirit of $\delta$-invariants, Decu et al. (2007) initiated the study of $\delta$-Casorati curvatures. Since then there are many interesting results on $\delta$-Casorati curvatures obtained by many authors. In this article we provide a comprehensive survey on recent developments in $\delta$-Casorati curvatures done during the last decade.
Star Edge Coloring Of Graphs With Mad($G$)$, Kavita Pradeep
Star Edge Coloring Of Graphs With Mad($G$)$, Kavita Pradeep
Turkish Journal of Mathematics
A star edge coloring of a graph $G$ is a proper edge coloring such that there is no bicolored path or cycle of length four. The minimum number of colors needed for a graph $G$ to admit a star edge coloring is called the star chromatic index and it is denoted by $\chi_s^{'}(G)$. In this paper, we consider graphs of maximum degree $\Delta \geq 4$ and show that if the maximum average degree of a graph is less than $\frac{14}{5}$ then $\chi_s^{'}(G) \leq 2\Delta + 1$.
On The Growth Of Maximum Modulus Of Rational Functions With Prescribed Poles, Lubna Wali Shah
On The Growth Of Maximum Modulus Of Rational Functions With Prescribed Poles, Lubna Wali Shah
Turkish Journal of Mathematics
In this paper we prove a sharp growth estimate for rational functions with prescribed poles and restricted zeros in the Chebyshev norm on the unit disk in the complex domain. In particular we extend a polynomial inequality due to Dubinin (2007) to rational functions which also improves a result of Govil and Mohapatra (1998).
On Neutrosophic Soft Continuous Mappings, Taha Yasi̇n Öztürk, Eli̇f Karataş, Adem Yolcu
On Neutrosophic Soft Continuous Mappings, Taha Yasi̇n Öztürk, Eli̇f Karataş, Adem Yolcu
Turkish Journal of Mathematics
In this paper, the concept of neutrosophic soft continuous mapping, neutrosophic soft open mapping, neutrosophic soft closed mapping and neutrosophic soft homeomorphism have been introduced along with the investigation of their several characteristics, and verified by proper examples.
Notes On Product Semisymmetric Connection In A Locally Decomposable Riemannian Space, Miroslav Maksimovic, Mica Stankovic
Notes On Product Semisymmetric Connection In A Locally Decomposable Riemannian Space, Miroslav Maksimovic, Mica Stankovic
Turkish Journal of Mathematics
The purpose of this paper is to investigate the product semisymmetric connection in a locally decomposable Riemannian space. The curvature tensors of this connection were considered. Some properties of almost product structure, some properties of torsion tensor of product semisymmetric connection and some relations between curvature tensors and almost product structure are given. Also, the paper checks a special case of such connection when its generator is a gradient vector.
On The Generalization Of $ \Kappa $-Fractional Hilfer-Katugampola Derivative With Cauchy Problem, Samaira Naz, Muhammad Nawaz Naeem
On The Generalization Of $ \Kappa $-Fractional Hilfer-Katugampola Derivative With Cauchy Problem, Samaira Naz, Muhammad Nawaz Naeem
Turkish Journal of Mathematics
We generalize the $\kappa$-fractional Hilfer--Katugampola derivative and set some properties of the generalized operator resulting from this. As an application, we demonstrate that the Cauchy problem with this new definition is equivalent to a second kind of Volterra integral equation. We discuss some specific cases for this problem.
Closure Operators In Convergence Approach Spaces, Muhammad Qasim, Mehmet Baran, Hassan Abughalwa
Closure Operators In Convergence Approach Spaces, Muhammad Qasim, Mehmet Baran, Hassan Abughalwa
Turkish Journal of Mathematics
In this paper, we characterize closed and strongly closed subsets of convergence approach spaces and introduce two notions of closure in the category of convergence approach spaces which satisfy idempotent, productive and (weakly) hereditary properties. Furthermore, we explicitly characterize each of $T_{i}$ convergence approach spaces, $i=0,1,2$ with respect to these closure operators and show that each of these subcategories of $T_{i}$ convergence approach spaces, $i=0,1,2$ are epireflective as well as we investigate the relationship among these subcategories. Finally, we characterize connected convergence approach spaces.
Existence Of A Positive Solution For A Singular Fractional Boundary Value Problem With Fractional Boundary Conditions Using Convolution And Lower Order Problems, Jeffrey W. Lyons, Jeffrey T. Neugebauer
Existence Of A Positive Solution For A Singular Fractional Boundary Value Problem With Fractional Boundary Conditions Using Convolution And Lower Order Problems, Jeffrey W. Lyons, Jeffrey T. Neugebauer
Turkish Journal of Mathematics
Existence of a positive solution is shown for two singular two-point fractional boundary value problems with fractional boundary conditions using fixed point theory, lower order problems, and convolution of Green's functions. A nontrivial example is included.
Quasi-Cesaro Matrix And Associated Sequence Spaces, Hadi Roopaei, Taja Yaying
Quasi-Cesaro Matrix And Associated Sequence Spaces, Hadi Roopaei, Taja Yaying
Turkish Journal of Mathematics
In the present study, we construct a new matrix which we call quasi-Cesaro matrix and is a generalization of the ordinary Cesaro matrix, and introduce $BK$-spaces $C^q_k$ and $C^q_{\infty}$ as the domain of the quasi-Cesaro matrix $C^q$ in the spaces $\ell_k$ and $\ell_{\infty},$ respectively. Furthermore, we exhibit some topological properties and inclusion relations related to these newly defined spaces. We determine the basis of the space $C^q_k$ and obtain Köthe duals of the spaces $C^q_k$ and $C^q_{\infty}.$ Based on the newly defined matrix, we present a factorization for the Hilbert matrix and generalize Hardy's inequality, as an application. Moreover we …
Widths And Entropy Of Sets Of Smooth Functions On Compact Homogeneous Manifolds, Alexander Kushpel, Kenan Taş, Jeremy Levesley
Widths And Entropy Of Sets Of Smooth Functions On Compact Homogeneous Manifolds, Alexander Kushpel, Kenan Taş, Jeremy Levesley
Turkish Journal of Mathematics
We develop a general method to calculate entropy and $n$-widths of sets of smooth functions on an arbitrary compact homogeneous Riemannian manifold $% \mathbb{M}^{d}$. Our method is essentially based on a detailed study of geometric characteristics of norms induced by subspaces of harmonics on $% \mathbb{M}^{d}$. This approach has been developed in the cycle of works [1, 2, 10-19]. The method's possibilities are not confined to the statements proved but can be applied in studying more general problems. As an application, we establish sharp orders of entropy and $n$-widths of Sobolev's classes $W_{p}^{\gamma }\left( \mathbb{M}^{d}\right) $ and their generalisations in …
Number Fields And Divisible Groups Via Model Theor, Şermi̇n Çam Çeli̇k, Haydar Göral
Number Fields And Divisible Groups Via Model Theor, Şermi̇n Çam Çeli̇k, Haydar Göral
Turkish Journal of Mathematics
In this note, we first show that solutions of certain equations classify the number fields lying in imaginary quadratic number fields. Then, we study divisible groups with a predicate. We show that these structures are not simple and have the independence property under some natural assumptions.
A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Niichel, Sabrina Streipert
A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Niichel, Sabrina Streipert
Turkish Journal of Mathematics
We investigate a family of probability distributions, with three parameters associated with the dynamic Gompertz function. We prove its existence for various parameter sets and discuss the existence of its time scale moments. Afterwards, we investigate the special case of discrete time scales, where it is shown that the discrete Gompertz distribution is a $q$-geometric distribution of the second kind. Further, we find their $q$-binomial moments, we bound their expected value, and we show how a classical Gompertz distribution is obtained from them.
Rotating Periodic Integrable Solutions For Second-Order Differential Systems With Nonresonance Condition, Yi Cheng, Ke Jin, Ravi Agarwal
Rotating Periodic Integrable Solutions For Second-Order Differential Systems With Nonresonance Condition, Yi Cheng, Ke Jin, Ravi Agarwal
Turkish Journal of Mathematics
In this paper, by using Parseval's formula and Schauder's fixed point theorem, we prove the existence and uniqueness of rotating periodic integrable solution of the second-order system $x''+f(t,x)=0$ with $x(t+T)=Qx(t)$ and $\int_{(k-1)T}^{kT}x(s)ds=0$, $k\in Z^+$ for any orthogonal matrix $Q$ when the nonlinearity $f$ satisfies nonresonance condition.
Polyhedral Optimization Of Second-Order Discrete And Differential Inclusions With Delay, Sevi̇lay Demi̇r Sağlam, Eli̇mhan N. Mahmudov
Polyhedral Optimization Of Second-Order Discrete And Differential Inclusions With Delay, Sevi̇lay Demi̇r Sağlam, Eli̇mhan N. Mahmudov
Turkish Journal of Mathematics
he present paper studies the optimal control theory of second-order polyhedral delay discrete and delay differential inclusions with state constraints. We formulate the conditions of optimality for the problems with the second-order polyhedral delay discrete $(PD_d)$ and the delay differential $(PC_d)$ in terms of the Euler-Lagrange inclusions and the distinctive ''transversality'' conditions. Moreover, some linear control problem with second-order delay differential inclusions is given to illustrate the effectiveness and usefulness of the main theoretic results.
A New Gauss--Newton-Like Method For Nonlinear Equations, Haijun Wang, Qi Wang
A New Gauss--Newton-Like Method For Nonlinear Equations, Haijun Wang, Qi Wang
Turkish Journal of Mathematics
In this paper, a new Gauss-Newton-like method that is based on a rational approximation model with linear numerator is proposed for solving nonlinear equations. The new method revises the $J_k^\mathrm{T}J_k$ matrix by a rank-one matrix at each iteration. Furthermore, we design a new iterative algorithm for nonlinear equations and prove that it is locally q-quadratically convergent. The numerical results show that the new proposed method has better performance than the classical Gauss-Newton method.
Generalized Littlewood-Paley Functions On Product Spaces, Hussain Alqassem, Leslie Cheng, Yibiao Pan
Generalized Littlewood-Paley Functions On Product Spaces, Hussain Alqassem, Leslie Cheng, Yibiao Pan
Turkish Journal of Mathematics
We are interested in investigating the $L^{p}$ boundedness of the product of generalized Littlewood-Paley functions $S_{\Phi }^{(\lambda )}(f)$ arising from kernels satisfying only size and cancellation conditions. We obtain $L^{p}$ estimates of $S_{\Phi }^{(\lambda )}(f)$ for a sharp range of $p$ and under optimal conditions on $\Phi $. Using these estimates and an extrapolation argument, we obtain some new and improved results on generalized Littlewood-Paley functions on product spaces. As a consequence of our main results, we get two results, one of which answers a question posed by D. Fan and H. Wu and the other one answers a question …
Self-Adjoint Extensions For A Class Of Singular Operators, Rauf Ami̇rov, Hidayat Mehmetoğlu Huseynov, Sevi̇m Durak
Self-Adjoint Extensions For A Class Of Singular Operators, Rauf Ami̇rov, Hidayat Mehmetoğlu Huseynov, Sevi̇m Durak
Turkish Journal of Mathematics
In this study, we consider the domains of the minimal and maximal operators generated of singular differential-expression-type Sturm-Liouville and obtain all self-adjoint extensions of the operator in terms of boundary conditions.
On $Q$- And $H$-Deformations Of 3d-Superspaces, Sali̇h Çeli̇k
On $Q$- And $H$-Deformations Of 3d-Superspaces, Sali̇h Çeli̇k
Turkish Journal of Mathematics
In this paper, we introduce nonstandard deformations of (1+2)- and (2+1)-superspaces via a contraction using standard deformations of them. This deformed superspaces are denoted by ${\mathbb A}_h^{1 2}$ and ${\mathbb A}_{h'}^{2 1}$, respectively. We find a two-parameter $R$-matrix satisfying quantum Yang--Baxter equation and thus obtain a { new} two-parameter nonstandard deformation of the supergroup ${\rm GL}(1 2)$. Finally, we get a new superalgebra derived from the Hopf superalgebra of functions on the quantum superspace ${\mathbb A}_{p,q}^{1 2}$.
Traces And Inverse Nodal Problems For A Class Of Delay Sturm-Liouville Operators, Erdoğan Şen
Traces And Inverse Nodal Problems For A Class Of Delay Sturm-Liouville Operators, Erdoğan Şen
Turkish Journal of Mathematics
In this study, we investigate the regularized sums of eigenvalues, oscillation of eigenfunctions and solutions of inverse nodal problems of discontinuous Sturm-Liouville operators with a delayed argument and with a finite number of transmission conditions. With this aim, we obtain asymptotic formulas for eigenvalues, eigenfunctions and nodal points of the problem. Moreover, some numerical examples are given to illustrate the results. The problem differs from the other discontinuous Sturm-Liouville problems with retarded argument in that it contains a spectral parameter in boundary conditions. If we take the delayed argument $\Delta\equiv0$, the coefficients $\alpha _{i}^{+}=\beta _{i}^{+}=0$ ($i=1,2$) in boundary conditions and …
On $F$-Kenmotsu $3$-Manifolds With Respect To The Schouten-Van Kampen Connection, Selcen Yüksel Perktaş, Ahmet Yildiz
On $F$-Kenmotsu $3$-Manifolds With Respect To The Schouten-Van Kampen Connection, Selcen Yüksel Perktaş, Ahmet Yildiz
Turkish Journal of Mathematics
In this paper we study some semisymmetry conditions and some soliton types on $f$-Kenmotsu $3$-manifolds with respect to the Schouten-van Kampen connection.
Peiffer Pairings In Multisimplicial Groups And Crossed $N$-Cubes And Applications For Bisimplicial Groups, Özgün Gürmen Alansal, Erdal Ulualan
Peiffer Pairings In Multisimplicial Groups And Crossed $N$-Cubes And Applications For Bisimplicial Groups, Özgün Gürmen Alansal, Erdal Ulualan
Turkish Journal of Mathematics
We explore the Peiffer pairings within the Moore complex of multisimplicial groups, and as an application, we give a detailed construction of a crossed $n$- cube from an $n$-simplicial group in terms of these pairings. We also give explicit calculations of Peiffer pairings in the Moore bicomplex of a bisimplicial group to see the role of these pairings in the relationship between bisimplicial groups and crossed squares.
Crossed Product Of Infinite Groups And Complete Rewriting Systems, Esra Kirmizi Çeti̇nalp, Eylem Güzel Karpuz
Crossed Product Of Infinite Groups And Complete Rewriting Systems, Esra Kirmizi Çeti̇nalp, Eylem Güzel Karpuz
Turkish Journal of Mathematics
The aim of this paper is to obtain a presentation for crossed product of some infinite groups and then find its complete rewriting system. Hence, we present normal form structure of elements of crossed product of infinite groups which yield solvability of the word problem.
On The Number Of Non-$G$-Equivalent Minimal Abelian Codes, Fatma Altunbulak Aksu, İpek Tuvay
On The Number Of Non-$G$-Equivalent Minimal Abelian Codes, Fatma Altunbulak Aksu, İpek Tuvay
Turkish Journal of Mathematics
Let $G$ be a finite abelian group. Ferraz, Guerreiro, and Polcino Milies (2014) proved that the number of $G$-equivalence classes of minimal abelian codes is equal to the number of $G$-isomorphism classes of subgroups for which corresponding quotients are cyclic. In this article, we prove that the notion of $G$-isomorphism is equivalent to the notion of isomorphism on the set of all subgroups $H$ of $G$ with the property that $G/H$ is cyclic. As an application, we calculate the number of non-$G$-equivalent minimal abelian codes for some specific family of abelian groups. We also prove that the number of non-$G$-equivalent …
On Some Topological Properties In The Class Of Alexandroff Spaces, Sami Lazaar, Houssem Sabri, Randa Tahri
On Some Topological Properties In The Class Of Alexandroff Spaces, Sami Lazaar, Houssem Sabri, Randa Tahri
Turkish Journal of Mathematics
In the class of Alexandroff spaces we study the properties of being a submaximal, door, Whyburn and weakly Whyburn space. We provide characterizations in order theoretical terms. Connections with posets, counting formulas and numerical results in the class of finite spaces are also given.