Browsing by Author "Taş, Kenan"

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A generalized contraction principle with control functions on partial metric spaces
(Pergamon-Elsevier Science Ltd, 2012) Abdeljawad, Thabet; Karapınar, Erdal; Taş, Kenan; 19184; 4971
Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions phi and psi on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions
A Gregus type common fixed point theorem of set-valued mappings in cone metric spaces
(Eudoxus Press, 2011) Abdeljawad, Thabet; Taş, Kenan; Taş, Kenan; 4971
The main purpose of this paper is to obtain a common fixed point theorem for a pair of set-valued mappings of Gregus type condition in cone metric spaces, so that the main result obtained in [13] will be generalized to cone metric spaces. The cone under consideration will be normal with normal constant K = 1
A New Class of Contraction in B -Metric Spaces and Applications
(Hindawi Limited, 2017) Taş, Kenan; Kaushik, P.; Kumar, S.; 4971
A novel class of α-β-contraction for a pair of mappings is introduced in the setting of b-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation.
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 new transform method in nabla discrete fractional calculus
(Springer International Publishing, 2012) Jarad, Fahd; Kaymakçalan, Billur; Taş, Kenan; 4971
Starting from the definition of the Sumudu transform on a general nabla time scale, we define the generalized nabla discrete Sumudu transform. We obtain the nabla discrete Sumudu transform of Taylor monomials, fractional sums, and differences. We apply this transform to solve some fractional difference equations with initial value problems.
A unique common triple fixed point theorem for hybrid pair of maps
(Hindawi Publishing Corporation, 2012) Taş, Kenan; Kishore, G. N. V.; Taş, Kenan; 4971
We obtain a unique common triple fixed point theorem for hybrid pair of mappings in metric spaces. Our result extends the recent results of B. Samet and C. Vetro (2011). We also introduced a suitable example supporting our result
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.
Advances on Fixed Point Results on Partial Metric Spaces
(2019) Karapınar, Erdal; Taş, Kenan; Rakocevic, Vladimir; 1918; 4971
In this note, we shall consider recent advances and improvements on fixed point theory in the setting of partial metric spaces. We investigate the existence and uniqueness of several distinct type contractive mapping in the context of complete partial metric space. We also recollect sum existing results to give complete survey for this topic.
An original coupled coincidence point result for a pair of mappings without MMP
(Springer International Publishing, 2014) Taş, Kenan; Taş, Kenan; 4971
The purpose of this paper is to establish a coupled coincidence point theorem for a pair of mappings without MMP (mixed monotone property) in metric spaces endowed with partial order, which is not an immediate consequence of a well-known theorem in the literature. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend some of the results of Bhaskar and Lakshmikantham (Nonlinear Anal. 65: 1379-1393, 2006), Choudhury, Metiya and Kundu (Ann. Univ. Ferrara 57:1-16, 2011), Harjani, Lopez and Sadarangani (Nonlinear Anal. 74:1749-1760, 2011) and of Luong and Thuan (Bull. Math. Anal. Appl. 2:16-24, 2010) for the mappings having no MMP. We introduce an example that there exists a common coupled fixed point of the mappings g and F such that F does not satisfy the g-mixed monotone property, and also g and F do not commute.
Application of sumudu and double sumudu transforms to caputo-fractional differential equations
(Eudoxus Press, 2012) Jarad, Fahd; Taş, Kenan; 4971
The definition, properties and applications of the Sumudu transform to ordinary differential equations are described in [1-3]. In this manuscript we derive the formulae for the Sumudu and double Sumudu transforms of ordinary and partial fractional derivatives and apply them in solving Caputo-fractional differential equations. Our purpose here is to show the applicability of this new transform and its efficiency in solving such problems
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.
Best proximity point theorems for KT-types cyclic orbital contraction mappings
(House Book Science, 2012) Karapınar, Erdal; Taş, Kenan; Taş, Kenan; 19184; 4971
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.
Chemometric calibration based on the wavelet transform for the quantitative resolution of two-colorant mixtures
(Editura Academiei Romane, 2005) Baleanu, Dumitru; Taş, Kenan; Üstündağ, O.; Taş, Kenan; 56389; 4971
In this study we proposed a wavelet transform (WT) followed by two chemometric techniques for the quantitative determination of sunset yellow (SUN) and tartrazine (TAR) in their market samples. Absorbances of the concentration set formed by TAR and SUN mixtures were measured between 335-575 nm at 480 points with 0.5 nm intervals and their absorbance values as absorbance data vectors were transferred into the wavelets domain. A continuous wavelet transform (CWT) was applied, to the absorbance data. The obtained CWT-coefficients (x-block) and concentration set (y-block) were used for the construction of the principal component regression (VCR) and partial least squares (PLS) calibrations. Good results were reported for the application of the combining wavelets and chemometric tools in the determination of colorants in samples.
Coincidence and Fixed Points of Non-expansive Type Mappings on 2-Metric Spaces
(2007) Taş, Kenan; Dubey, Sweetee; Taş, Kenan; 4971
In this paper a unique coincidence value is obtained for a class of self mappings satisfying non-expansive type condition on 2-metric spaces under various conditions and a fixed point theorem is also obtained.
Common fixed point theorems for generalized (phi,psi)-weak contraction condition in complete metric spaces
(2015) Taş, Kenan; Taş, Kenan; Patel, Uma Devi; 4971
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.
Common fixed point theorems for generalized (phi,psi)-weak contraction condition in complete metric spaces
(Springer, 2015) Taş, Kenan; Taş, Kenan; Patel, Uma Devi; 4971
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
Common fixed point theorems in cone Banach spaces
(2011) Abdeljawad, Thabet; Karapınar, Erdal; Taş, Kenan; 4971
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.
Common fixed point theorems in cone banach spaces
(Hacettepe Üniversitesi, Fac Sci, 2011) Abdeljawad, Thabet; Karapınar, Erdal; Taş, Kenan; 19184; 4971
Recently, E. Karapinar (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.
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 points of self maps satisfying an integral type contractive condition in fuzzy metric spaces
(Univ Osijek, Depth Mathematics, 2010) Taş, Kenan; Kumar, Sanjay; Taş, Kenan; 4971
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