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On Fractional P-Laplacian Type Equations With General Nonlinearities, Adel Daouas, Mohamed Louchaich
On Fractional P-Laplacian Type Equations With General Nonlinearities, Adel Daouas, Mohamed Louchaich
Turkish Journal of Mathematics
In this paper, we study the existence and multiplicity of solutions for a class of quasi-linear elliptic problems driven by a nonlocal integro-differential operator with homogeneous Dirichlet boundary conditions. As a particular case, we study the following problem: \begin{equation*} \left\{ \begin{array}{l} (-\Delta)_p^s u= f(x,u) \quad \hfill \textrm{in} \ \Omega,\\ \quad u=0 \ \hfill \textrm{in} \ R^N \setminus \Omega, \end{array} \right.\\ \end{equation*} where $(-\Delta)_p^s$ is the fractional p-Laplacian operator, $\Omega$ is an open bounded subset of $R^N$ with Lipschitz boundary and $f:\Omega \times R \to R$ is a generic Carath\'eodory function satisfying either a $p-$sublinear or a $p-$superlinear growth condition.
Non-Singular Cubic Surfaces Over $\Mathbb{F}_{2^K}$, Fatma Karaoğlu
Non-Singular Cubic Surfaces Over $\Mathbb{F}_{2^K}$, Fatma Karaoğlu
Turkish Journal of Mathematics
We perform an opportunistic search for cubic surfaces over small fields of characteristic two. The starting point of our work is a list of surfaces complied by Dickson over the field with two elements. We consider the nonsingular ones arising in Dickson' s work for the fields of larger orders of characteristic two. We investigate the properties such as the number of lines, singularities and automorphism groups. The problem of determining the possible numbers of lines of a nonsingular cubic surface over the fields of $\mathbb{C}, \mathbb{R}, \mathbb{Q}, \mathbb{F}_q$ where q odd, $\mathbb{F}_2$ was considered by Cayley and Salmon, Schlafli, …
Decompositions Of Semigroups, Rida E. Zenab
Decompositions Of Semigroups, Rida E. Zenab
Turkish Journal of Mathematics
In this article we discuss the factorisations of semigroups and monoids in the context of direct, semidirect and Zappa-Szep products addressing the question of uniqueness. An equivalence between external and internal Zappa-Szep product of groups and monoids is known, but no such correspondence exists for semigroups in general. We prove the equivalence between external and internal Zappa-Szep product of semigroups subject to certain conditions in this article. We end with some illustrative examples of the Zappa-Szep product of the bisimple inverse monoids.
Linear Stability Of Periodic Standing Waves Of The Kgz System, Sevdzhan Ahmedov Hakkaev, Fati̇h Hunutlu
Linear Stability Of Periodic Standing Waves Of The Kgz System, Sevdzhan Ahmedov Hakkaev, Fati̇h Hunutlu
Turkish Journal of Mathematics
In this work we consider the periodic standing wave solutions for a Klein-Gordon-Zakharov system. We find the conditions on the parameters, for which the periodic waves of dnoidal type are linear stable/unstable.
Higher Cohomologies For Presheaves Of Commutative Monoids, Pilar Carrasco, Antonio M. Cegarra
Higher Cohomologies For Presheaves Of Commutative Monoids, Pilar Carrasco, Antonio M. Cegarra
Turkish Journal of Mathematics
We present an extension of the classical Eilenberg-MacLane higher order cohomology theories of abelian groups to presheaves of commutative monoids (and of abelian groups, then) over an arbitrary small category. These high-level cohomologies enjoy many desirable properties and the paper aims to explore them. The results apply directly in several settings such as presheaves of commutative monoids on a topological space, simplicial commutative monoids, presheaves of simplicial commutative monoids on a topological space, commutative monoids or simplicial commutative monoids on which a fixed monoid or group acts, and so forth. As a main application, we state and prove a precise …
On Lyapunov-Type Inequalities For $(N+1)$St Order Nonlinear Differential Equations With The Anti-Periodic Boundary Conditions, Mustafa Fahri̇ Aktaş
On Lyapunov-Type Inequalities For $(N+1)$St Order Nonlinear Differential Equations With The Anti-Periodic Boundary Conditions, Mustafa Fahri̇ Aktaş
Turkish Journal of Mathematics
In this paper, we establish new Lyapunov-type inequalities for $\left(n+1\right)$st order nonlinear differential equation including $p$-relativistic operator and $q$-prescribed curvature operator under the antiperiodic boundary conditions.
Generating Finite Coxeter Groups With Elements Of The Same Order, Sarah B. Hart, Veronica Kelsey, Peter Rowley
Generating Finite Coxeter Groups With Elements Of The Same Order, Sarah B. Hart, Veronica Kelsey, Peter Rowley
Turkish Journal of Mathematics
Supposing $G$ is a group and $k$ a natural number, $d_k(G)$ is defined to be the minimal number of elements of $G$ of order $k$ which generate $G$ (setting $d_k(G)=0$ if $G$ has no such generating sets). This paper investigates $d_k(G)$ when $G$ is a finite Coxeter group either of type $B_n$ or $D_n$, or of exceptional type. Together with the work of Garzoni and Yu, this determines $d_k(G)$ for all finite irreducible Coxeter groups $G$ when $2 \leq k \leq (G)$ ($(G)+1$ when $G$ is of type A$_{n}$).
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.