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https://hdl.handle.net/20.500.12587/18876

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Best proximity and best periodic points for proximal nonunique contractions
(Springer Basel Ag, 2021) Şahin, Hakan; Aslantaş, Mustafa; Altun, İshak
Taking into account nonunique fixed point and periodic point results of Ciric (Institut Mathematique 17, 52-58, 1974) and best proximity point results in the literature, we introduce the concept of proximal nonunique contraction for nonself mappings. Then, we obtain some nonunique best proximity point theorems. Further, we describe the concept of best periodic point of nonself mappings and we present some nonunique best periodic point results. We also provide many examples to show that our new concepts are meaningful and to support our theorems. Additionally, we present a new notion for the nonself mapping H called property P-b, and then we provide some results including sufficient conditions to guarantee that H has the property P-b.
Approximation by Some Baskakov-Kantorovich Exponential-Type Operators
(Springer Singapore Pte Ltd, 2022) Özsaraç, Fırat; Gupta, Vijay; Aral, Ali
In the present paper, we propose the modification of the Baskakov-Kantorovich operators based on mu-integral. Such operators are connected with exponential functions. We estimate moments and establish some direct results in terms of modulus of continuity.
Approximation of operators related to squared Sza acute accent sz-Mirakjan basis functions
(Univ Nis, Fac Sci Math, 2023) Rahman, Shagufta; Aral, Ali; Mursaleen, M.
The main objective of this paper is to define a sequence of positive linear operators by means of the squared Szasz-Mirakjan basis functions. We estimate the rate of convergence in terms of the modulus of continuity and the class of Lipschitz functions. Furthermore, we have shown the comparison and convergence of these operators with the help of some illustrative graphics.
Approximation Results for Hadamard-Type Exponential Sampling Kantorovich Series
(Springer Basel Ag, 2023) Kurşun, Sadettin; Aral, Ali; Acar, Tuncer
The present paper deals with construction of a new family of exponential sampling Kantorovich operators based on a suitable fractional-type integral operators. We study convergence properties of newly constructed operators and give a quantitative form of the rate of convergence thanks to logarithmic modulus of continuity. To obtain an asymptotic formula in the sense of Voronovskaja, we consider locally regular functions. The rest of the paper devoted to approximations of newly constructed operators in logarithmic weighted space of functions. By utilizing a suitable weighted logarithmic modulus of continuity, we obtain a rate of convergence and give a quantitative form of Voronovskaja-type theorem via remainder of Mellin-Taylor's formula. Furthermore, some examples of kernels which satisfy certain assumptions are presented and the results are examined by illustrative numerical tables and graphical representations.
Approximation properties of modified Jain-Gamma operators
(Vasyl Stefanyk Precarpathian Natl Univ, 2021) Erdoğan, S.; Olgun, A.
In the present paper, we study some approximation properties of a modified Jain-Gamma operator. Using Korovkin type theorem, we first give approximation properties of such operator. Secondly, we compute the rate of convergence of this operator bymeans of themodulus of continuity and we present approximation properties of weighted spaces. Finally, we obtain the Voronovskaya type theorem of this operator.
A new approach to curve couples with Bishop frame
(Ankara Univ, Fac Sci, 2024) Babadağ, Faik; Atasoy, Ali
. This paper presents a detailed study of a new generation of the Bishop frame with components including three orthogonal unit vectors, which are tangent vector, normal vector and binormal vector. It is a frame field described on a curve in Euclidean space, which is an alternative to the Frenet frame. It is useful for curves for which the second derivative is not available. Moreover, the conditions which the Bishop frame of one curve coincides with the Bishop frame of another curve are defined. It would be valuable to replicate similar approaches in the Bishop frame of one curve coincides with the Bishop frame of another curve.
On The Mellin-Gauss-Weierstrass Operators In The Mellin-Lebesgue Spaces
(Ankara Univ, Fac Sci, 2024) Özsaraç, Fırat
In this paper, we present the modulus of smoothness of a function f is an element of X-c(p), which the Mellin-Lebesgue space, and later we state some properties of it. In this way, the rate of convergence is gained. Moreover, we elucidate some pointwise convergence results for the Mellin-Gauss-Weierstrass operators. Especially, we acquire the pointwise convergence of them at any Lebesgue point of a function f.
Cholesky Algorithm Of A Lucas Type Matrix
(Ankara Univ, Fac Sci, 2024) Yılmaz, Semih; Erdoğan, Betül
Many generalizations have been made for Fibonacci and Lucas number sequences and many properties have been found about these sequences. In the article [13], the authors obtained many features of these sequences with the Cholesky decomposition algorithm, using the 2 x 2 matrix belonging to a generalization of the Fibonacci sequence. In this study, it is shown that many different features can be found by using a 2 x 2 matrix belonging to the Lucas number sequence with the same method.
Neumann boundary value problem for the Beltrami equation in a ring domain
(Tubitak Scientific & Technological Research Council Turkey, 2023) Gençtürk, İlker
In this paper, the Neumann boundary value problem for the Beltrami operator is explicitly solved in a circular ring domain, solvability conditions for this problem are also given in explicit forms. Moreover, the Neumann problem for second-order operators with the Bitsadze/Laplace operator as the main part as combinations of the Cauchy-Riemann and the Beltrami operators is investigated.
The inequalities on dual numbers and their topological structures
(Tubitak Scientific & Technological Research Council Turkey, 2023) Aktaş, Büşra; Durmaz, Olgun; Gündoğan, Halit
Inequalities are frequently used in various fields of mathematics to prove theorems. The existence of inequalities contributes significantly to the foundations of such branches. In this paper, we study the properties of order relations in the system of dual numbers, which is inspired by order relations defined on real numbers. Besides, some special inequalities that are used in various fields of mathematics, such as Cauchy-Schwarz, Minkowski, and Chebyshev are studied in this framework. An example is also provided to validate our research findings.
On Some Approximation Properties Of The Gauss-Weierstrass Operators
(2019) Yılmaz, Başar
In this paper, we present some approximation properties of the Gauss-Weierstrass operators in exponential weighted spaces including norm convergence of them and Voronovskaya and quantitative Voronovskaya-type theorems.
Approximation of Class of Non-linear Integral Operators
(2017) Almalı, Sevgi Esen
In this study,we investigate the problem of pointwise convergence at lebesgue points of funtions for the family of non-linear integral operators L,(f,x) f’”(t)Km(x,t)dt mil where fl, is real parameter, (x, t) is non-negative kernels and is the function in L1(a, b) We consider two cases where (a b) is finite interval and when is the whole real axis.
A family of incomplete hurwitz-lerch zeta functions of two variables
(University of Miskolc, 2020) Srivastava H.M.; Şahin R.; Yağci O.
Inspired essentially by the work [H. M. Srivastava, M. A. Chaudhry and R. P. Agarwal [The incomplete Pochhammer symbols and their applications to hypergeometric and related functions, Integral Transforms Spec. Funct. 23 (2012), 659-683] (see [16])], we introduce the families of the incomplete Hurwitz-Lerch Zeta functions of two variables. We then give the integral representations including the Mellin-Barnes contour integral representation, summation formulas, derivative formulas and recurrence relations for the incomplete Hurwitz-Lerch Zeta functions of two variables. © 2020 Miskolc University Press.
Multidimensional Bilinear Hardy Inequalities
(INST MATH & MECHANICS AZERBAIJAN, 2020) Bilgicli, N.; Mustafayev, R. Ch; Unver, T.
Our goal in this paper is to find a characterization of n-dimensional bilinear Hardy inequalities parallel to integral(B(0,.)) f.integral(B(0,.)) g parallel to(q,u(0,infinity) )<= C parallel to f parallel to(p1,v1,Rn)parallel to g parallel to(p2,v2,Rn), f, g is an element of M+(R-n), parallel to integral c(B(0,.)) f.integral c(B(0,.)) g parallel to(q,u(0,infinity) )<= C parallel to f parallel to(p1,v1,Rn)parallel to g parallel to(p2,v2,Rn), f, g is an element of M+(R-n), when 0 < q <= infinity, 1 <= p1, p2 <= infinity and u and v1, v 2 are weight functions on (0,infinity ) and , R-n, respectively. Obtained results are new when p(i) = 1 or p(i) =infinity, i = 1, 2, or 0 < q <= 1 even in 1-dimensional case. Since the solution of the first inequality can be obtained from the characterization of the second one by usual change of variables we concentrate our attention on characterization of the latter. The characterization of this inequality is easily obtained for p(1) <= q using the characterizations of multidimensional weighted Hardy-type inequalities while in the case q < p(1) the problem is reduced to the solution of multidimensional weighted iterated Hardy-type inequality. To achieve our goal, we characterize the validity of multidimensional weighted iterated Hardy-type inequality parallel to parallel to integral cB((0,s)) h(z)dz parallel to(p,u,(0,t))parallel to(q,mu,(0,infinity) <= c parallel to h parallel to(theta,v,(0,infinity),) h is an element of M+(R-n) where 0 < p, q < infinity, 1 <= theta <= infinity, u is an element of W (0, infinity ), v is an element of W(R-n) and mu is a non-negative Borel measure on (0, infinity). We are able to obtain the characterization under the additional condition that the measure mu is non-degenerate with respect to U-q/p.
On Nonlinear Set-Valued theta-Contractions
(MALAYSIAN MATHEMATICAL SCIENCES SOC, 2020) Durmaz, Gonca; Altun, Ishak
In this paper, we introduce and study new fixed point results for nonlinear set-valued theta-contractions. Our results are based on a new approach, which is called set-valued theta-contraction and they extend and generalize many fixed point theorems in the literature.
On The Basic Structures Of Dual Space
(UNIV NIS, 2020) Aktas, Busra; Durmaz, Olgun; Gundogan, Halit
Topology studies the properties of spaces that are invariant under any continuous deformation. Topology is needed to examine the properties of the space. Fundamentally, the most basic structure required to do math in the space is topology. There exists little information on the expression of the basis and topology on dual space. The main point of the research is to explain how to define the basis and topology on dual space D-n. Then, we will study the geometric constructions corresponding to the open balls in D and D-2, respectively.
New Approaches On Dual Space
(UNIV NIS, 2020) Durmaz, Olgun; Aktas, Busra; Gundogan, Halit
In this paper, we have explained how to define the basic concepts of differential geometry on Dual space. To support this, dual tangent vectors that have (p) over bar as dual point of application have been defined. Then, the dual analytic functions defined by Dimentberg have been examined in detail, and by using the derivative of the these functions, dual directional derivatives and dual tangent maps have been introduced.
Some Characterizations Of Generalized Null Mannheim Curves In Semi-Euclidean Space
(INST BIOPHYSICS & BIOMEDICAL ENGINEERING, BULGARIAN ACAD SCIENCES, 2020) Aslan, Nihal Kılıç; İlarslan, Kazım
In the present paper, we investigate Cartan framed generalized null Mannheim curves in the four-dimensional semi-Euclidean space of index two. We construct the Cartan (or Frenet) frames and curvature functions of generalized Mannheim mate curve with the help of curvatures and Cartan frames of generalized null Mannheim curve.
Fixed point results for single valued and set valued P-contractions and application to second order boundary value problems
(NORTH UNIV BAIA MARE, 2020) Altun, Ishak; Hancer, Hatice Aslan; Erduran, Ali
In this paper, by considering the concept of set-valued nonlinear P-contraction which is newly introduced, we present some new fixed point theorems for set-valued mappings on complete metric space. Then by considering a single-valued case we provide an existence and uniqueness result for a kind of second order two point boundary value problem.
On Parallelizable Spheres in Semi Euclidean Space
(SOUTHEAST ASIAN MATHEMATICAL SOC-SEAMS, 2020) Durmaz, Olgun; Aktas, Busra; Gundogan, Halit
In Euclidean space, there exist four theorems which show that S-n sphere is not parallelizable for n not equal 1, 3, 7. While three of them are shown by using Bott theorem, the last one is shown by using Hurwitz-Radon numbers. In this paper, a theorem and the proof of this theorem about parallelization of spheres in semi-Euclidean space is given. It is presented that some spheres are parallelizable with respect to specific number systems.

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