Browsing by Author "Taş, Kenan"

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Citation - WoS: 5
Citation - Scopus: 6
Application of Sumudu and Double Sumudu Transforms To Caputo-Fractional Differential Equations
(Eudoxus Press, Llc, 2012) Jarad, Fahd; Jarad, Fahd; Tas, K.; Taş, Kenan; 4971; Matematik
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.
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
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 Acad Romane, 2005) Baleanu, Dumitru; Dinç, E; Baleanu, D; Taş, Kenan; Üstundag, O; Tas, K; 56389; 4971; Matematik
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) Namdeo, R.K.; 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
(Springer, 2015) Murthy, Penumarthy Parvateesam; 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.
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
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.
Continuous wavelet analysis for the ratio signals of the absorption spectra of binary mixtures
(Springer, 2007) Dinç, Erdal; Baleanu, Dumitru; Taş, Kenan; 56389
Wavelet analysis is successfully applied to the quantitative determination of the components in the binary mixture. This mathematical application is based on the use of the division of the absorption signals by the standard absorption signal and the transformation of the ratio signals. Calibration functions are obtained by measuring the continuous wavelet amplitudes corresponding to the minimum points of the wavelengths. The method is validated and applied to one example of binary mixture analysis.
Citation - WoS: 7
Citation - Scopus: 7
Coupled Fixed Point Theorems for Generalized Symmetric Contractions in Partially Ordered Metric Spaces and Applications
(Eudoxus Press, Llc, 2014) Jain, M.; Taş, Kenan; Tas, K.; Rhoades, B. E.; Gupta, N.; 4971; Matematik
In the setting of partially ordered metric spaces, we introduce the notion of generalized symmetric g-Meir-Keeler type contractions and use the notion to establish the existence and uniqueness of coupled common fixed points. Our notion extends the notion of generalized symmetric Meir-Keeler contractions given by Berinde et. al. [V. Berinde, and M. Pacurar, Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces, Fixed Point Theory and Appl., 2012, 2012:115, doi:10.1186/1687-1812-2012-115] to a pair of mappings. We also give some applications of our main 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
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.
Generalized (C)-conditions and related fixed point theorems
(Pergamon-Elsevier Science Ltd, 2011) Karapınar, Erdal; Taş, Kenan; 19184; 42699
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.
Citation - WoS: 3
Citation - Scopus: 4
A Gregus Type Common Fixed Point Theorem of Set-Valued Mappings in Cone Metric Spaces
(Eudoxus Press, Llc, 2011) Abdeljawad, Thabet; Abdeljawad, T.; Murthy, P. P.; Taş, Kenan; Tas, K.; 4971; Matematik
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.
On Singular Fifth-Order Boundary Value Problems With Deficiency Indices (5, 5)
(Math Soc Serbia-drustvo Matematicara Srbije, 2022) Uğurlu, Ekin; Ugurlu, Ekin; Tas, Kenan; Taş, Kenan; 238990; Matematik
This paper is devoted to introduce a way of construction of the well-defined boundary conditions for the solutions of a singular fifth-order equation with deficiency indices (5, 5). Imposing suitable separated and coupled boundary conditions some properties of the eigenvalues of the problems have been investigated.
On the composition of the distributions x(+)(-r) and x(+)(mu)
(Indian Nat Sci Acad, 2005) Fisher, Brian; Taş, Kenan; Takaci, A.; 4971
Let F be a distirbution and let f be a locally summable function. The distribution F (f) is defined as the neutrix limit of the sequence {F-n(f)}, where F-n(x) = F(x) (*) delta(n)(x) and {delta(n)(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta function delta(x). The distribution (x(+)(mu))(-r)(+) and (1 x 1(mu))(-r)(+) are evaluated for mu > 0, r = 1, 2,..., and k mu not equal 1, 2,....
On the composition of the distributions x(+)(-r) and x(+)(mu)
(2005) Fisher, B.; Taş, Kenan; 4971
Let F be a distirbution and let f be a locally summable function. The distribution F (f) is defined as the neutrix limit of the sequence {F-n(f)}, where F-n(x) = F(x) (*) delta(n)(x) and {delta(n)(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta function delta(x). The distribution (x(+)(mu))(-r)(+) and (1 x 1(mu))(-r)(+) are evaluated for mu > 0, r = 1, 2,..., and k mu not equal 1, 2,....
On the composition of the distributions x(-1) ln vertical bar x vertical bar and x(+)(r)
(2005) Fisher, B.; Taş, Kenan; 4971
Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F-n(f)}, where F-n(x) = F(x) * delta(n)(x) and {delta(n)(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function (x). The distribution (x(+)(r))(-1) ln \x(+)(r)\ is evaluated for r = 1, 2.....
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; 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 non-commutative neutrix product of the distributions x(+)(lambda) and x(+)(mu)
(Springer Heidelberg, 2006) Fisher, Brian; Taş, Kenan; 4971
Let f and g be distributions and let 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 circle g of f and g is defined to be the limit of the sequence {fg(n)}, provided its limit h exists in the sense that [GRAPHICS] for all functions p in D. It is proved that (x(+)(lambda)ln(p)x(+)) circle (x(+)(mu)ln(q)x(+)) = x(+)(lambda+mu)ln(p+q)x(+), (x(-)(lambda)ln(p)x(-)) circle (x(-)mu ln(q)x(-)) = x(-)(lambda+mu)ln(p+q)x(-), for lambda + mu < -1; lambda,mu,lambda+mu not equal -1,-2,... and p,q = 0,1,2.....
On the Non-Commutative Neutrix Product of the Distributions xλ + and xμ +
(Springer Science & Business Media B.V., 2006) Fisher, Brian; Taş, Kenan; 4971
Let f and g be distributions and let gn = (g ∗ δn)(x), where δn(x) is a certain sequence converging to the Dirac delta function. The non-commutative neutrix product f ◦g of f and g is defined to be the limit of the sequence {fgn}, provided its limit h exists in the sense that N−lim n→∞ f(x)gn(x), ϕ(x) = h(x), ϕ(x) , for all functions ϕ in D. It is proved that (xλ + lnp x+) ◦ (xμ + lnq x+) = xλ+μ + lnp+q x+, (xλ − lnp x−) ◦ (xμ − lnq x−) = xλ+μ − lnp+q x−, for λ + μ < −1; λ, μ, λ + μ = −1, −2,... and p, q = 0, 1, 2.... .
On the solutions of a fractional boundary value problem
(2018) Uğurlu, Ekin; Baleanu, Dumitru; Taş, Kenan; 56389; 4971; 238990
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.