Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
20 results
Search Results
Correction Citation - WoS: 12Common Fixed Point Theorems in Modified Intuitionistic Fuzzy Metric Spaces (Vol 2013, 189321, 2013)(Hindawi Publishing Corporation, 2014) Manro, Saurabh; Kumar, Sanjay; Bhatia, S. S.; Tas, KenanArticle Citation - WoS: 3Citation - Scopus: 3On the Characteristic Functions and Dirchlet-Integrable Solutions of Singular Left-Definite Hamiltonian Systems(Taylor & Francis Ltd, 2024) Ugurlu, Ekin; Bairamov, Elgiz; Tas, KenanIn this work, a singular left-definite Hamiltonian system is considered and the characteristic-matrix theory for this Hamiltonian system is constructed. Using the results of this theory we introduce a lower bound for the number of Dirichlet-integrable solutions. Moreover we share a relation between the kernel of the solution of the nonhomogeneous boundary value problem and the characteristic-matrix.Article Citation - WoS: 1Scattering and Characteristic Functions of a Dissipative Operator Generated by a System of Equations(Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Bayram, Elgiz; Tas, KenanIn 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-Foias model operator theory we prove a completeness theorem.Article Citation - WoS: 3Citation - Scopus: 3Quadruple Fixed Point Theorems for Nonlinear Contractions on Partial Metric Spaces(Univ Politecnica Valencia, Editorial Upv, 2014) Karapinar, Erdal; Tas, KenanThe notion of coupled fixed point was introduced by Guo and Laksmikantham [12]. Later Gnana Bhaskar and Lakshmikantham in [11] investigated the coupled fixed points in the setting of partially ordered set by defining the notion of mixed monotone property. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut [7]. Following this trend, Karapmar[19] defined the quadruple fixed point. In this manuscript, quadruple fixed point is discussed and some new fixed point theorems are obtained on partial metric spaces.Article Citation - WoS: 1Citation - Scopus: 1On the Non-Commutative Neutrix Product of the Distributions X<sup>-r</Sup>+ Ln<sup>p</Sup> X+ and X<sup>μ</Sup>+ln<sup>q< X+(Taylor & Francis Ltd, 2006) Tas, Kenan; Fisher, BrianLet f and g be distributions and g(n) = (g*delta(n))(x), where delta(n)(x ) is a certain sequence converging to the Dirac delta-function. The non-commutative neutrix product f o g of f and g is defined to be the neutrix limit of the sequence {fg(n) }, provided its limit h exists in the sense that [GRAPHICS] for all functions phi in D. It is proved that (x(+)(-r) ln(p) x(+)) o (x(+)(mu) ln(q) x(+)) = x(+)(-r+mu) ln(p+q) x(+) (x(-)(-r) ln(p) (x)-) o (x(-)(mu) ln(q) x(-)) = x(-)(-r+mu) ln(p+q) x(-) for mu < r - 1;mu not equal 0, +/- 1, +/- 2,..., r = 1,2,..., and p, q = 0, 1, 2,....Article On a Fifth-Order Nonselfadjoint Boundary Value Problem(Tubitak Scientific & Technological Research Council Turkey, 2021) Ugurlu, Ekin; Tas, KenanIn this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative operator. In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipativeArticle Citation - WoS: 5Citation - Scopus: 5Widths and Entropy of Sets of Smooth Functions on Compact Homogeneous Manifolds(Tubitak Scientific & Technological Research Council Turkey, 2021) Levesley, Jeremy; Tas, Kenan; Kushpel, AlexanderWe develop a general method to calculate entropy and n-widths of sets of smooth functions on an arbitrary\rcompact homogeneous Riemannian manifold Md\r. Our method is essentially based on a detailed study of geometric\rcharacteristics of norms induced by subspaces of harmonics on Md\r. This approach has been developed in the cycle\rof works [1, 2, 10–19]. The method’s possibilities are not confined to the statements proved but can be applied in\rstudying more general problems. As an application, we establish sharp orders of entropy and n-widths of Sobolev’s\rclasses Wγ\rp\r(\rMd\r)\rand their generalisations in Lq\r(\rMd\r)\rfor any 1 < p, q < ∞. In the case p, q = 1, ∞ sharp in the power\rscale estimates are presented.Article Citation - WoS: 1Citation - Scopus: 1Fractional Differential Equation With a Complex Potential(Univ Nis, Fac Sci Math, 2020) Ugurlu, Ekin; Tas, Kenan; Baleanu, DumitruIn this manuscript, we discuss the square-integrable property of a fractional differential equation having a complex-valued potential function and we show that at least one of the linearly independent solutions of the fractional differential equation must be squarely integrable with respect to some function containing the imaginary parts of the spectral parameter and the potential function.Article Citation - WoS: 3Citation - Scopus: 3Dissipative Operator and Its Cayley Transform(2017) Tas, Kenan; Uğurlu, EkinIn this paper, we investigate the spectral properties of the maximal dissipative extension of the minimal symmetric differential operator generated by a second order differential expression and dissipative and eigenparameter dependent boundary conditions. For this purpose we use the characteristic function of the maximal dissipative operator and inverse operator. This investigation is done by the characteristic function of the Cayley transform of the maximal dissipative operator, which is a completely nonunitary contraction belonging to the class C0. Using Solomyak s method we also introduce the self-adjoint dilation of the maximal dissipative operator and incoming/outgoing eigenfunctions of the dilation. Moreover, we investigate other properties of the Cayley transform of the maximal dissipative operator.Article Citation - WoS: 8Citation - Scopus: 11On the Solutions of a Fractional Boundary Value Problem(Tubitak Scientific & Technological Research Council Turkey, 2018) Ugurlu, Ekin; Baleanu, Dumitru; Tas, KenanThis paper is devoted to showing the existence and uniqueness of solution of a regular second-order nonlinear fractional differential equation subject to the ordinary boundary conditions. The Banach fixed point theorem is used to prove the results.