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Öğe A NOTE ON KANTOROVICH TYPE BERNSTEIN CHLODOVSKY OPERATORS WHICH PRESERVE EXPONENTIAL FUNCTION(Element, 2021) Aral, Ali; Ari, Didem Aydin; Yilmaz, BasarThis paper is mainly focused on the integral extension of Bernstein-Chlodovsky operators which preserve exponential function. Inspire of the Bernstein-Chlodovsky operators which preserve exponential function, we define the integral extension of these operators by using a different technique. We give weighted approximation properties including a weighted uniform convergence and a weighted quantitative theorem in terms of exponential weighted modulus of continuity. Furthermore, we give the Voronovskaya type theorem.Öğe A note on Kantorovich Type Bernstein Chlodovsky Operators which Preserve Exponential Function(Element D.O.O., 2021) Aral, Ali; Ari, Didem Aydin; Yilmaz, Bas¸arThis paper is mainly focused on the integral extension of Bernstein-Chlodovsky operators which preserve exponential function. Inspire of the Bernstein-Chlodovsky operators which preserve exponential function, we define the integral extension of these operators by using a different technique. We give weighted approximation properties including a weighted uniform convergence and a weighted quantitative theorem in terms of exponential weighted modulus of continuity. Furthermore, we give the Voronovskaya type theorem. © 2021. Journal of Mathematical Inequalities. All rights reserved.Öğe Applications of (p,q)-gamma function to Szász Durrmeyer operators(Publications L Institut Mathematique Matematicki, 2017) Aral, Ali; Gupta, VijayWe define a (p, q) analogue of Gamma function. As an application, we propose (p, q)-Szasz-Durrmeyer operators, estimate moments and establish some direct results.Öğe Approximating by Szsz-Type operators(Vsp Bv-C/O Brill Acad Publ, 2005) Aral, Ali; Erbay, HasanWe introduce a new Szasz-Type operators depending on weighted functions. We analyze approximation results of these operators on weighted space. Our numerical results are consistent with our theory.Öğe Approximation by baskakov-szász-stancu operators preserving exponential functions(Selcuk University, 2018) Bodur, Murat; Yilmaz, Övgü Gürel; Aral, AliThe purpose of this paper is to construct a general class of operators which has known Baskakov- Szász-Stancu that preserving constant and e2ax; a > 0 functions. We scrutinize a uniform convergence result and analyze the asymptotic behavior of our operators, as well. Finally, we discuss the convergence of corresponding sequences in exponential weighted spaces and make a comparison about which one approximates better between classical Baskakov-Szász-Stancu operators and the recent operators. © 2018 Selcuk University. All right reserved.Öğe Approximation by Bivariate (p, q)-Bernstein-Kantorovich Operators(Springer International Publishing Ag, 2018) Acar, Tuncer; Aral, Ali; Mohiuddine, S. A.In the present paper, we introduce Kantorovich modifications of (p, q)-Bernstein operators for bivariate functions using a new (p, q)-integral. We first estimate the moments and central moments. We give the uniform convergence of new operators, rate of convergence in terms of modulus of continuity. The approximations behaviours of the operators for functions having continuous partial derivatives and for functions belong to Lipschitz class are investigated as well.Öğe Approximation by k-th order modifications of Szász-Mirakyan operators(Akademiai Kiado Rt, 2016) Acar, Tuncer; Aral, Ali; Rasa, IoanIn this paper, we study the k-th order Kantorovich type modication of Szasz-Mirakyan operators. We first establish explicit formulas giving the images of monomials and the moments up to order six. Using this modification, we present a quantitative Voronovskaya theorem for differentiated Szasz-Mirakyan operators in weighted spaces. The approximation properties such as rate of convergence and simultaneous approximation by the new constructions are also obtained.Öğe Approximation by q Baskakov Beta operators(Springer Heidelberg, 2011) Gupta, Vijay; Aral, AliIn the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, a). Then we obtain point-wise estimate, using the Lipschitz type maximal function.Öğe Approximation by sampling Kantorovich series in weighted spaces of functions(Tubitak Scientific & Technological Research Council Turkey, 2022) Acar, Tuncer; Alagoz, Osman; Aral, Ali; Costarelli, Danilo; Turgay, Metin; Vinti, GianlucaThis paper studies the convergence of the so-called sampling Kantorovich operators for functions belonging to weighted spaces of continuous functions. This setting allows us to establish uniform convergence results for functions that are not necessarily uniformly continuous and bounded on R. In that context we also prove quantitative estimates for the rate of convergence of the family of the above operators in terms of weighted modulus of continuity. Finally, pointwise convergence results in quantitative form by means of Voronovskaja type theorems have been also established.Öğe Approximation by Some Baskakov-Kantorovich Exponential-Type Operators(Springer Singapore Pte Ltd, 2022) Özsaraç, Fırat; Gupta, Vijay; Aral, AliIn 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.Öğe 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.Öğe Approximation of operators related to squared Szász-Mirakjan basis functions(University of Nis, 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 Szász-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. © 2023, University of Nis. All rights reserved.Öğe Approximation properties of Kantorovich extension of Ibragimov-Gadjiev Operators(2005) Aral, AliIn this paper we deal with Kantorovich extension of Ibragimov-Gadjiev Operators. We give pointwise approximation of these operators. We also establish Voronovskaya type theorem in the polynomial weighted spaces for these operators.Öğe Approximation properties of Szasz-Mirakyan operators preserving exponential functions(Springer, 2019) Aral, Ali; Inoan, Daniela; Rasa, IoanThis paper is a natural continuation of Acar et al. (Mediterr J Math 14:6, 2017, 10.1007/s00009-016-0804-7) where Szasz-Mirakyan operators preserving exponential functions are defined. As a first result, we show that the sequence of the norms of the operators, acting on weighted spaces having different weights, is uniformly bounded. Then, we prove Korovkin type approximation theorems through exponential weighted convergence. The uniform weighted approximation errors of the operators and their derivatives are characterized for exponential weights. Furthermore we give a Voronovskaya type theorem for the derivative of the operators.Öğe Approximation properties of Szasz-Mirakyan-Kantorovich type operators(Wiley, 2019) Aral, Ali; Limmam, Mohamed Lemine; Ozsarac, FiratIn this paper, we introduce and study new type Szasz-Mirakyan-Kantorovich operators using a technique different from classical one. This allow to analyze the mentioned operators in terms of exponential test functions instead of the usual polynomial type functions. As a first result, we prove Korovkin type approximation theorems through exponential weighted convergence. The rate of convergence of the operators is obtained for exponential weights.Öğe APPROXIMATION PROPERTIES OF TWO DIMENSIONAL BERNSTEIN-STANCU-CHLODOWSKY OPERATORS(Univ Studi Catania, Dipt Matematica, 2013) Acar, Tuncer; Aral, AliIn this paper, as a generalization of Bernstein-Stancu type operators of two variable, we introduce a new positive linear operator C-n (alpha,alpha,beta,beta,) (f; x, y) called Bernstein-Stancu-Chlodowsky on a triangular domain, with mobile boundaries, which extends to [0,infinity) x [0,infinity) as n -> infinity. We give some shape properties that are preserved and also obtain weighted approximation properties of these operators.Öğe Approximation Results for Hadamard-Type Exponential Sampling Kantorovich Series(Springer Basel Ag, 2023) Kurşun, Sadettin; Aral, Ali; Acar, TuncerThe 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.Öğe Bernstein durrmeyer operators based on two parameters(Univ Nis, 2016) Gupta, Vijay; Aral, AliIn the present paper, we study the applications of the extension of quantum calculus based on two parameters. We define beta function and establish an identity with gamma function, for two parameters (p, q), ie. the post-quantum calculus. We also propose the (p, q)-Durrmeyer operators, estimate moments and establish some direct results. Depending on the selection of p and q, the rate of convergence of the our new operators can provide better approximation than those of the Bernstein-Durrmeyer operators and its q-analogue. In the end, we provide some graphs using the software Mathematica.Öğe Bernstein-Type Operators That Reproduce Exponential Functions(Element, 2018) Aral, Ali; Cardenas-Morales, Daniel; Garrancho, PedroIn this paper we recover a generalization of the classical Bernstein operators introduced by Morigi and Neamtu in 2000. Specifically, we focus on a sequence of operators that reproduce the exponential functions exp(mu t) and exp(2 mu t), mu > 0. We study its convergence, this including qualitative and quantitative theorems, an asymptotic formula and saturation results. We also show their shape preserving properties by considering generalized convexity. Finally, a comparison is stated, that shows that in a certain sense and for certain family of illustrative functions the new sequence approximates better than the classical Bernstein polynomials.Öğe Bir ve iki değişkenli bernstein-stancu-chlodowsky polinomlarının yaklaşım özellikleri(2013) Aral, Ali; Acar, Tuncer; Yıldız, Duygu Döndü[Abstract Not Available]
