Browsing by Author "Tas, Kenan"

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Citation - WoS: 5
Advances on Fixed Point Results on Partial Metric Spaces
(Springer international Publishing Ag, 2019) Rakocevic, Vladimir; Karapinar, Erdal; Tas, Kenan; 1918; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 7
Citation - Scopus: 13
Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case
(Mdpi, 2019) Gordievskikh, Dmitriy M.; Tas, Kenan; Baleanu, Dumitru; Fedorov, Vladimir E.; 4971; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 19
Citation - Scopus: 18
Best Proximity Point Theorems for Kt-Types Cyclic Orbital Contraction Mappings
(House Book Science-casa Cartii Stiinta, 2012) Karapınar, Erdal; Karapinar, Erdal; Petrusel, Gabriela; Taş, Kenan; Tas, Kenan; 19184; 4971; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript, three new KT-types cyclic orbital contractions are defined and some related best proximity point theorems are given. Also, the notion of KT-type cyclic orbital Meir-Keeler contraction is defined and some fixed point theorems for this class of mappings are proved. The results of this manuscript generalize some theorems, on the same subject, of several authors, such as Kirk-Srinavasan-Veeramani, Eldered-Veeramani and Karpagam-Agrawal.
Citation - WoS: 7
Citation - Scopus: 9
Common Fixed Point Theorems for Generalized (φ,ψ)-Weak Contraction Condition in Complete Metric Spaces
(Springer international Publishing Ag, 2015) Tas, Kenan; Patel, Uma Devi; Murthy, Penumarthy Parvateesam; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The intent of this manuscript is to establish some common fixed point theorems in a complete metric space under weak contraction condition for two pairs of discontinuous weak compatible maps. The results proved herein are the generalization of some recent results in literature. We give an example to support our results.
Citation - WoS: 16
Citation - Scopus: 20
Common Fixed Point Theorems in Cone Banach Spaces
(Hacettepe Univ, Fac Sci, 2011) Abdeljawad, Thabet; Tas, Kenan; Karapınar, Erdal; 19184; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Recently, E. Karapınar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.
Citation - WoS: 1
Citation - Scopus: 3
Common Fixed Point Theorems in Modified Intuitionistic Fuzzy Metric Spaces
(Hindawi Ltd, 2013) Kumar, Sanjay; Bhatia, S. S.; Tas, Kenan; Manro, Saurabh; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 12
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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 11
Citation - Scopus: 18
Common Fixed Points of Self Maps Satisfying an Integral Type Contractive Condition in Fuzzy Metric Spaces
(Univ Osijek, dept Mathematics, 2010) Murthy, Penumarthy Parvateesam; Taş, Kenan; Kumar, Sanjay; Tas, Kenan; 4971; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, first we prove fixed point theorems for different variant of compatible maps, satisfying a contractive condition of integral type in fuzzy metric spaces, which improve the results of Branciari [2], Rhoades [33], Kumar et al .[23], Subramanyam [35] and results of various authors cited in the literature of "Fixed Point Theory and Applications". Secondly, we introduce the notion of any kind of weakly compatible maps and prove a fixed point theorem for weakly compatible maps along with the notion of any kind of weakly compatible. At the end, we prove a fixed point theorem using variants of R-Weakly commuting mappings in fuzzy metric spaces.
Commutative Convolution of Functions and Distributions
(Taylor & Francis Ltd, 2007) Tas, Kenan; Fisher, Brian; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 2
Citation - Scopus: 1
Coupled Common Fixed Point Results Involving (φ,ψ)-Contractions in Ordered Generalized Metric Spaces With Application To Integral Equations
(Springeropen, 2013) Tas, Kenan; Gupta, Neetu; Jain, Manish; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 16
Citation - Scopus: 8
Coupled Common Fixed Point Results Involving a (φ,ψ)-Contractive Condition for Mixed G-Monotone Operators in Partially Ordered Metric Spaces
(Springeropen, 2012) Tas, Kenan; Kumar, Sanjay; Gupta, Neetu; Jain, Manish; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the setting of partially ordered metric spaces, using the notion of compatible mappings, we establish the existence and uniqueness of coupled common fixed points involving a (phi,psi)-contractive condition for mixed g-monotone operators. Our results extend and generalize the well- known results of Berinde (Nonlinear Anal. TMA 74: 7347-7355, 2011; Nonlinear Anal. TMA 75:3218-3228, 2012) and weaken the contractive conditions involved in the results of Alotaibi et al. (Fixed Point Theory Appl. 2011: 44, 2011), Bhaskar et al. (Nonlinear Anal. TMA 65:1379-1393, 2006), and Luong et al. (Nonlinear Anal. TMA 74:983-992, 2011). The effectiveness of the presented work is validated with the help of suitable examples.
Citation - WoS: 30
Citation - Scopus: 28
Coupled Fixed Point Theorems for a Pair of Weakly Compatible Maps Along With Clrg Property in Fuzzy Metric Spaces
(Hindawi Publishing Corporation, 2012) Tas, Kenan; Kumar, Sanjay; Gupta, Neetu; Jain, Manish; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The aim of this paper is to extend the notions of E. A. property and CLRg property for coupled mappings and use these notions to generalize the recent results of Xin-Qi Hu (2011). The main result is supported by a suitable example.
Coupled Fixed Points in Complex Partial Metric Spaces
(int Scientific Research Publications, 2022) Khan, M. S.; Singh, Y. Mahendra; Tas, Kenan; Gunaseelan, M.; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we obtain coupled fixed point theorems in complex partial metric spaces under the different contractive conditions. Examples are provided to support our results.
Citation - WoS: 1
Citation - Scopus: 1
Dependence of Eigenvalues of Some Boundary Value Problems
(Tsing Hua Univ, dept Mathematics, 2021) Uğurlu, Ekin; Ugurlu, Ekin; Tas, Kenan; Taş, Kenan; 4971; 238990; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work we deal with a system of two first-order differential equations containing the same eigenvalue parameter. We consider some suitable separated real and complex coupled boundary conditions, and show that the eigenvalues generated by this system are continuous in an eigenvalue branch. Also we introduce the ordinary and Frechet derivatives of these eigenvalues with respect to some elements of the data.
Citation - WoS: 3
Citation - Scopus: 3
Dissipative Operator and Its Cayley Transform
(2017) Tas, Kenan; Uğurlu, Ekin; 4971; 238990; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 34
Fixed Point Theorem on Partial Metric Spaces Involving Rational Expressions
(Univ Miskolc inst Math, 2013) Tas, Kenan; Karapinar, Erdal; Shatanawi, Wasfi; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 11
Citation - Scopus: 15
Fixed Points for Cyclic Orbital Generalized Contractions on Complete Metric Spaces
(de Gruyter Open Ltd, 2013) Tas, Kenan; Karapinar, Erdal; Romaguera, Salvador; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 1
Citation - Scopus: 1
Fractional Differential Equation With a Complex Potential
(Univ Nis, Fac Sci Math, 2020) Ugurlu, Ekin; Tas, Kenan; Baleanu, Dumitru; 238990; 4971; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 68
Citation - Scopus: 69
Fractional Hamiltonian Analysis of Higher Order Derivatives Systems
(Aip Publishing, 2006) Tas, Kenan; Baleanu, Dumitru; Muslih, Sami I.; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 4
Citation - Scopus: 4
Fractional Wavelet Analysis of the Composite Signals of Two-Component Mixture by Multivariate Spectral Calibration
(Sage Publications Ltd, 2007) Baleanu, Dumitru; Tas, Kenan; Dinc, Erdal; 6981; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.