Browsing by Author "Tas, Kenan"

Now showing 1 - 18 of 18

A new method for dissipative dynamic operator with transmission conditions
(Springer Basel Ag, 2018) Uğurlu, Ekin; Ugurlu, Ekin; Tas, Kenan; Taş, Kenan; 238990; 4971
In this paper, we investigate the spectral properties of a boundary value transmission problem generated by a dynamic equation on the union of two time scales. For such an analysis we assign a suitable dynamic operator which is in limit-circle case at infinity. We also show that this operator is a simple maximal dissipative operator. Constructing the inverse operator we obtain some information about the spectrum of the dissipative operator. Moreover, using the Cayley transform of the dissipative operator we pass to the contractive operator which is of the class With the aid of the minimal function we obtain more information on the dissipative operator. Finally, we investigate other properties of the contraction such that multiplicity of the contraction, unitary colligation with basic operator and CMV matrix representation associated with the contraction.
A Unique Coupled Common Fixed Point Theorem for Symmetric (P,P) -Contractive Mappings in Ordered G -Metric Spaces With Applications
(Hindawi Ltd, 2013) Jain, Manish; Taş, Kenan; Tas, Kenan; 4971
We establish the existence and uniqueness of coupled common fixed point for symmetric (phi, psi)-contractive mappings in the framework of ordered G-metric spaces. Present work extends, generalize, and enrich the recent results of Choudhury and Maity (2011), Nashine (2012), and Mohiuddine and Alotaibi (2012), thereby, weakening the involved contractive conditions. Our theoretical results are accompanied by suitable examples and an application to integral equations.
Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case
(Mdpi, 2019) Baleanu, Dumitru; Baleanu, Dumitru; Fedorov, Vladimir E.; Taş, Kenan; Gordievskikh, Dmitriy M.; Tas, Kenan; 4971; 56389
We consider a class of linear inhomogeneous equations in a Banach space not solvable with respect to the fractional Caputo derivative. Such equations are called degenerate. We study the case of the existence of a resolving operators family for the respective homogeneous equation, which is an analytic in a sector. The existence of a unique solution of the Cauchy problem and of the Showalter-Sidorov problem to the inhomogeneous degenerate equation is proved. We also derive the form of the solution. The approximate controllability of infinite-dimensional control systems, described by the equations of the considered class, is researched. An approximate controllability criterion for the degenerate fractional order control system is obtained. The criterion is illustrated by the application to a system, which is described by an initial-boundary value problem for a partial differential equation, not solvable with respect to the time-fractional derivative. As a corollary of general results, an approximate controllability criterion is obtained for the degenerate fractional order control system with a finite-dimensional input.
Common fixed point theorems in modified ıntuitionistic fuzzy metric spaces
(Hindawi Ltd, 2013) Manro, Saurabh; Taş, Kenan; Kumar, Sanjay; Bhatia, S. S.; Tas, Kenan; 4971
This paper consists of main two sections. In the first section, we prove a common fixed point theorem in modified intuitionistic fuzzy metric space by combining the ideas of pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions. In the second section, we prove common fixed point theorems in modified intuitionistic fuzzy metric space from the class of compatible continuous mappings to noncompatible and discontinuous mappings. Lastly, as an application, we prove fixed point theorems using weakly reciprocally continuous noncompatible self-mappings on modified intuitionistic fuzzy metric space satisfying some implicit relations.
Common 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, Kenan
Commutative convolution of functions and distributions
(Taylor & Francis Ltd, 2007) Fisher, Brian; Taş, Kenan; Tas, Kenan; 4971
The commutative convolution f * g of two distributions f and g in D' is defined as the limit of the sequence {(f tau(n)) * (g tau(n))}, provided the limit exists, where {tau(n)} is a certain sequence of functions tn in D converging to 1. It is proved that |x|(lambda) * (sgn x|x|(-lambda-1)) = pi[cot (pi lambda) - cosec(pi lambda)] sgn x|x|(0), for lambda not equal 0, +/- 1, +/- 2, ... , where B denotes the Beta function.
Coupled common fixed point results involving (Φ,Ψ)-contractions in ordered generalized metric spaces with application to integral equations
(Springeropen, 2013) Jain, Manish; Taş, Kenan; Tas, Kenan; Gupta, Neetu; 4971
We establish some coupled coincidence and coupled common fixed point theorems for the mixed g-monotone mappings satisfying -contractive conditions in the setting of ordered generalized metric spaces. Presented theorems extend and generalize the very recent results of Choudhury and Maity (Math. Comput. Model. 54(1-2):73-79, 2011). To illustrate our results, an example and an application to integral equations have also been given. MSC: 54H10, 54H25.
Fixed Point Theorem On Partial Metric Spaces Involving Rational Expressions
(Univ Miskolc inst Math, 2013) Karapınar, Erdal; Karapinar, Erdal; Shatanawi, Wasfi; Taş, Kenan; Tas, Kenan; 4971
We establish a fixed point theorem involving a rational expression in a complete partial metric space. Our result generalizes a well-known result in (usual) metric spaces. Also, we introduce an example to illustrate the usability of our result.
Fixed points for cyclic orbital generalized contractions on complete metric spaces
(de Gruyter Open Ltd, 2013) Karapınar, Erdal; Karapinar, Erdal; Romaguera, Salvador; Taş, Kenan; Tas, Kenan; 4971
We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293-303]. Our results generalize some theorems of Kirk, Srinavasan and Veeramani, and of Karpagam and Agrawal.
Fractional Hamiltonian analysis of higher order derivatives systems
(Aip Publishing, 2006) Baleanu, Dumitru; Baleanu, Dumitru; Muslih, Sami I.; Taş, Kenan; Tas, Kenan; 4971
The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives. (c) 2006 American Institute of Physics.
Fractional wavelet analysis of the composite signals of two-component mixture by multivariate spectral calibration
(Sage Publications Ltd, 2007) Dinc, Erdal; Baleanu, Dumitru; Baleanu, Dumitru; Tas, Kenan; 6981
The fractional wavelet transform is a new mathematical tool for signal and image analysis. In this study, fractional wavelet analysis of the composite signals of the components in a binary mixture was investigated. In the quantitative evaluation of hydrochlorothiazide and cilazapril, partial least squares calibration was applied to the fractional wavelet coefficients after optimization of the experimental conditions. The validation of the partial least squares approach was tested by analyzing various synthetic mixtures consisting of active compounds of interest. Hydrochlorothiazide and cilazapril in real samples were analyzed using partial least squares calibration based on the fractional wavelet coefficients without a prior chemical separation procedure. This combined method is a potential new chemometric approach and is suitable for quantitative analysis of the components in samples.
Generalized (C)-conditions and related fixed point theorems
(Pergamon-elsevier Science Ltd, 2011) Karapınar, Erdal; Karapinar, Erdal; Tas, Kenan; Taş, Kenan; 19184; 4971
In this manuscript, the notion of C-condition [K. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095] is generalized. Some new fixed point theorems are obtained. (C) 2011 Elsevier Ltd. All rights reserved.
Generalized diamond-alpha dynamic opial inequalities
(Springer, 2012) Kaymakçalan, Billur; Atasever, Nuriye; Kaymakcalan, Billur; Taş, Kenan; Lesaja, Goran; Tas, Kenan; 4971
We establish some new dynamic Opial-type diamond alpha inequalities in time scales. Our results in special cases yield some of the recent results on Opial's inequality and also provide new estimates on inequalities of this type. Also, we introduce an example to illustrate our result.
Invariant approximation results via common fixed point theorems for generalized weak contraction maps
(Hindawi Ltd, 2014) Rathee, Savita; Taş, Kenan; Kumar, Anil; Tas, Kenan; 4971
A common fixed point theorem for generalized (phi,phi,L)(f,g)-weak contraction in a metric space is established. As an application, some common fixed point results in normed linear spaces are obtained. We also study some results on best approximation via common fixed point theorems. Our result improves some results from the existing literature. Some illustrative examples to highlight the realized improvements are also furnished.
On the non-commutative neutrix product of the distributions x(+)(-r) ln(p) x(+) and x(+)(mu)ln(q) x(+)
(Taylor & Francis Ltd, 2006) Fisher, Brian; Taş, Kenan; Tas, Kenan; 4971
Let 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,....
On the solutions of a fractional boundary value problem
(Tubitak Scientific & Technological Research Council Turkey, 2018) Uğurlu, Ekin; Ugurlu, Ekin; Baleanu, Dumitru; Baleanu, Dumitru; Tas, Kenan; Taş, Kenan; 238990; 56389; 4971
This 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.
Quadruple fixed point theorems for nonlinear contractions on partial metric spaces
(Univ Politecnica Valencia, Editorial Upv, 2014) Karapınar, Erdal; Karapinar, Erdal; Tas, Kenan; Taş, Kenan; 19184; 4971
The 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.
Regular fractional differential equations in the sobolev space
(Walter de Gruyter Gmbh, 2017) Uğurlu, Ekin; Ugurlu, Ekin; Baleanu, Dumitru; Baleanu, Dumitru; Tas, Kenan; Taş, Kenan; 238990; 56389; 4971
In this paper regular fractional Sturm-Liouville boundary value problems are considered. In particular, new inner products are described in the Sobolev space and a symmetric operator is established in this space.