Matematik Bölümü Koleksiyonu

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https://hdl.handle.net/20.500.12491/89

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On Hilbert-Pachpatte type inequalities within?-Hilfer fractional generalized derivatives
(Amer Inst Mathematical Sciences-Aims, 2023) Başçı, Yasemin; Baleanu, Dumitru
In this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided psi-Hilfer fractional derivatives with the general kernel. Our results are a generalization of the inequalities of Pecaric ' and Vukovic ' [1]. Furthermore, using the specific cases of the psi-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting psi, a1, b1 and considering the limit of the parameters alpha and beta.
Some convergence results for nonlinear Baskakov-Durrmeyer operators
(Carpathian Mathematical Publications, 2023) Altın, Hüseyin Ertan
This paper is an introduction to a sequence of nonlinear Baskakov-Durrmeyer operators (NBDn) of the form (NBDn) (f; x) =integral(infinity)(0) K-n(x, t, f (t)) dt with x is an element of [0, infinity) and n is an element of N. While Kn(x, t, u) provide convenient assumptions, these operators work on bounded functions, which are defined on all finite subintervals of [0, infinity). This paper comprise some pointwise convergence results for these operators in certain functional spaces. As well as this study can be seen as a continuation of studies about nonlinear operators, it is the first study on nonlinear Baskakov-Durrmeyer or modified Baskakov operators, while there were more papers on linear part of the operators.
On urysohn-chlodovsky operators acting on functions defined over the real line
(Springer Basel Ag, 2023) Karslı, Harun
As a continuation of the very recent studies of the author dealing with Urysohn type operators (Karsli in Results Math 72(3):1571- 1583, 2017; Karsli in Approximation Results for Urysohn Type Nonlinear Bernstein Operators, Advances in Summability and Approximation Theory, Springer, Singapore, 2018; Karsli in Math Methods Appl Sci 42(16):5190-5198, 2019; Karsli in Const Math Anal 1(1):45-57, 2018; Karsli in Stud Univ Babes Bolyai Math 64(2):183-196, 2019; Karsli in Dolomites Res Notes Approx 14(2):58-67, 2021; Karsli in Carpathian Math Publ 13(3):631-641, 2021) and Chlodovsky operators acting on functions defined over the real line (Abel and Karsli in Mediterr J Math 17:201, 2020; Karsli in Adv Oper Theory 7:15, 2022), the first main goal of this work is to introduce an Urysohn type Chlodovsky operators acting on functions defined over the real line using the Urysohn type interpolation of the given function f which is bounded on every finite subinterval of R. These operators include several operators, which are very useful in signal reconstruction and approximation theory. Afterwards, we will give some characterization and convergence results for these operators, which are generalization and extension of the theory of classical interpolation of functions to operators. Finally, we give some applications of our study with some graphical representations. As a special case of our operators and approaches, one can obtain the recent operators, defined on the symmetric interval [-1, 1], introduced and investigated by Demkiv and Barnetskij
A fixed point method for stability of nonlinear volterra integral equations in the sense of Ulam
(Wiley, 2022) Öğrekçi, Süleyman; Başcı, Yasemin; Mısır, Adil
In this paper, we investigate the Hyers-Ulam and Hyers-Ulam-Rassias stability of solutions of a general class of nonlinear Volterra integral equations. By applying a fixed point theorem and modifying a technique widely used in similar problems, we improve some well-known results on this problem. We also provide some examples illustrating the improvement of the results mentioned.
Numerical computing of isophote curves, general helices, and relatively normal-slant helices in Minkowski 3-space
(Wiley, 2022) Öztürk, Ufuk; Nesovic, Emilija; Öztürk, Esra Betül Koç
In this paper, we present a method for numerical computing of some characteristic kinds of non-null curves lying on a non-degenerate surface in Minkowski space 13. Namely, we obtain the system of the first-order ordinary differential equations that correspond to general helix, relatively normal-slant helix, and isophote curve and integrate it under chosen initial conditions by applying the ode45 function of MATLAB and Runge-Kutta method. Depending on the kind of curve, we assume that parametric equation of the surface, an axis vector, value of the real cosine or hyperbolic cosine of the corresponding pseudo angle between axis vector and Darboux frame's vector, normal curvature, and geodesic torsion of the curve are given. Finally, we provide the related examples of numerically computed characteristic curves.
Generalized derivatives and Laplace transform in(k, ? ) Hilfer form
(Wiley, 2023) Başcı, Yasemin; Mısır, Adil; Öğrekçi, Süleyman
In this work, we discuss the most generalized derivatives and integrals and their features in (k, psi)-Hilfer form. Furthermore, we define the new generalized Laplace transform to the generalized derivatives and integrals in (k, psi)-Hilfer form. Also, we have obtained the new generalized Laplace transforms of some expressions. These statements obtained cover many previous studies. Finally, we have given an example that will both use some of the results obtained and emphasize the importance of parameters such ask, rho, psi of the (k, psi)-generalized Laplace transform.
Rate of convergence of stancu type modified q-gamma operators for functions with derivatives of bounded variation
(Amer Inst Mathematical Sciences-Aims, 2023) Karslı, Harun; Agrawal, Purshottam Narain
Recently, Karsli [15] estimated the convergence rate of the q-Bernstein-Durrmeyer operators for functions whose q-derivatives are of bounded variation on the interval [0, 1]. Inspired by this study, in the present paper we deal with the convergence rate of a q- analogue of the Stancu type modified Gamma operators, defined by Karsli et al. [17], for the functions phi whose q-derivatives are of bounded variation on the interval [0, infinity). We present the approximation degree for the operator (S-n,l,q((alpha,beta)) phi) (3) at those points 3 at which the one sided q-derivatives D-q(+) phi(3) and D-q(-) phi(3) exist.
On the Hyers-Ulam stability of delay differential equations
(Georgian National Academy of Sciences, 2022) Öǧrekçi, Süleyman; Başcı, Yasemin; Mısır, Adil
In this paper, we consider the stability problem of delay differential equations in the sense of Hyers-Ulam and Hyers-Ulam-Rassias. By using a well known fixed point alternative on generalized complete metric spaces, we obtain some new stability criteria. Our results extend and improve the results described in literature since their proofs are based on fewer and weaker assumptions than the recent results dealing with this problem. Some illustrative examples are also given to compare these results and visualize the improvement.
Fixing a gap in laterally closed lattice homomorphisms
(Springer, 2022) Ercan, Zafer
A gap in the proof of the main result of the paper A remark on the paper 'Laterally closed lattice homomorphisms' is fixed.
A complete extension of the Bernstein-Weierstrass Theorem to the infinite interval (-?, +?) via Chlodovsky polynomials
(Springer, 2022) Karslı, Harun
In the present paper, we consider the very recently introduced Chlodovsky operators on the real line by Abel and Karsli (Mediterr J Math 17:201, 2020). We study some approximation properties of these new operators, which include the rate of convergence and a Voronovskaya type theorem.
On interpolative R-Meir-Keeler contractions of rational forms
(University of Nis, Faculty of Sciences and Mathematics, 2023) Öztürk, Ali
In this article, the notion of rational interpolative Meir-Keeler type contraction is discussed. The existence and uniqueness of a fixed point for interpolative Meir-Keeler contraction of rational Das-Gupta are investigated. The obtained results improve and generalize the existing results on the topic in the recent literature.
Gröbner-Shirshov basis and normal forms for the infinite Coxeter group of type ˜Cn
(Tbilisi Center for Mathematical Sciences, 2022) Ustaoğlu, Uğur; Yılmaz, Erol
A Gröbner-Shirshov basis and classification of the normal forms for the infinite Coxeter group of type (C) over tilde (n) are obtained. A new algorithm for getting normal forms of elements of this groups is also given.
On interpolative R-Meir-Keeler contractions of rational forms
(Yokohama Publ, 2022) Öztürk, Ali; Yeşilkaya, Seher Sultan
In this manuscript, the notion of rational interpolative Meir-Keeler type contraction is defined and discussed in the setting of complete metric spaces. The existence and uniqueness of a fixed point for such mappings are investigated. The obtained results improve and generalize the existing results on the topic in the recent literature.
Structures of exact solutions for the modified nonlinear Schrodinger equation in the sense of conformable fractional derivative
(Springer Heidelberg, 2023) Özkan, Yeşim Sağlam; Yılmaz, Esra Ünal
This paper is devoted to discuss analytically the conformable time-fractional modified nonlinear Schrodinger equation with the aid of efficient methods. The suggested model is a model used in ocean engineering to explain the propagation of water waves. At this stage, while using the proposed methods, the first step is to reduce the model defined by the conformable fractional derivative to the ordinary differential equation system with an appropriate transformation. We have obtained a variety of new families of exact traveling wave solutions including trigonometric, hyperbolic and exponential types. In related subject, the Adomian decomposition method is implemented to approximate the one of the solution of the underlying equation. For dynamic properties of the obtained solutions, we have depicted them graphically using computer programming to explain more efficiently the behavior of different shapes of solutions for the different values of free parameters with constraint conditions. Finally, a comparison is given for the solutions obtained in this study.
On generalized Darboux frame of a spacelike curve lying on a lightlike surface in Minkowski space E31 Dedicated to the memory of Professor Emeritus Krishan Lal Duggal
(Scientific and Technological Research Council Turkey, 2023) Djordjevic, Jelena; Nesovic, Emilija; Öztürk, Ufuk
In this paper we introduce generalized Darboux frame of a spacelike curve alpha lying on a lightlike surface in Minkowski space E31 . We prove that alpha has two such frames and obtain generalized Darboux frame's equations. We find the relations between the curvature functions kg, kn , tau g of alpha with respect to its Darboux frame and the curvature functions k similar to g, k similar to n , tau similar to g with respect to generalized Darboux frames. We show that such frames exist along a spacelike straight line lying on a ruled surface which is not entirely lightlike, but contains some lightlike points. We define lightlike ruled surfaces on which the tangent and the binormal indicatrix of a null Cartan curve are the principal curvature lines having tau similar to g = 0 and give some examples.
On Hilbert-Pachpatte type inequalities within ?-Hilfer fractional generalized derivatives
(American Institute of Mathematical Sciences-AIMS, 2023) Başcı, Yasemin; Baleanu, Dumitru
In this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided psi-Hilfer fractional derivatives with the general kernel. Our results are a generalization of the inequalities of Pecaric ' and Vukovic ' [1]. Furthermore, using the specific cases of the psi-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting psi, a1, b1 and considering the limit of the parameters alpha and beta.
Composition laws on the Fricke surface and Markov triples
(Scientific and Technological Research Council Turkey, 2022) Uludağ, Abdurrahman Muhammed; Yılmaz, Esra Ünal
We determine some composition laws related to the Fricke surface and the "double" Fricke surface. This latter surface admits the squares of Markov triples as its solutions.
Optical soliton solutions to eight order nonlinear Schrodinger equation using some different methods
(Springer, 2021) Yılmaz, Esra Ünal; Özkan, Yeşim Sağlam
In this study, the eight order nonlinear Schrodinger equation modeling the pulse propagation in optical fiber is discussed. Optical fibers is used for long-distance and high-performance data networking which making it the logical choice for data transmission. For this reason, it becomes important to examine these type equations. Three different useful and effective methods have been used to obtain optical soliton solutions of this equation. In addition, it is tried to give more information about the dynamic performance of the model with the help of three-dimensional graphics. Finally, the stability property of the obtained analytical solution was investigated based on Hamiltonian systems.
Some characterizations of pseudo null isophotic curves in Minkowski 3-space
(Springer Basel Ag, 2021) Nesovic, Emilija; Öztürk, Ufuk; Öztürk, Esra Betül Koç
In this paper, we define and characterize pseudo null isophotic curves lying on a non-degenerate surface in Minkowski 3-space. We find the relation between Darboux frame's Darboux vector (angular velocity vector, centrode) (D) over bar of such curves and Frenet frame's Darboux vector D. We prove that D spans their axes if and only if it coincides with (D) over bar. In particular, we show that the only pseudo null isophotic curves whose axes are spanned by D are pseudo null helices. Finally, we provide the related examples.
On multidimensional Urysohn type generalized sampling operators
(American Institute of Mathematical Sciences-AIMS, 2021) Karslı, Harun
The concern of this study is to construction of a multidimensional version of Urysohn type generalized sampling operators, whose one dimensional case defined and investigated by the author in [28] and [27]. In details, as a continuation of the studies of the author, the paper centers around to investigation of some approximation and asymptotic properties of the aforementioned linear multidimensional Urysohn type generalized sampling operators.

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