In this article, we introduce a modified class of bernstein-kantorovich operators dependingonan integrable function psi(alpha) and investigate their approximation properties. By choosing an appropriate function f, the...
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In this article, we introduce a modified class of bernstein-kantorovich operators dependingonan integrable function psi(alpha) and investigate their approximation properties. By choosing an appropriate function f, the order of approxi-mation of our operators to a function psi(alpha) is at least as good as the classical bernstein-kantorovich operators on the interval[0,1]. We compared the operators defined in this study not only with bernstein-kantorovich operators butalso with some other bernstein-kantorovich type operators. In this paper, wealso study the results on the uniform convergence and rate of convergenceof these operators in terms of the first- and second-order moduli of continuity, and we prove that our operators have shape-preserving properties. Finally,some numerical examples which support the results obtained in this paper areprovided.
In the present article, we study the approximation properties of constructed operators based on the shape parameter alpha. We construct the Stancu-type operators of alpha-bernstein-Schurer-kantorovichoperators. Here ...
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In the present article, we study the approximation properties of constructed operators based on the shape parameter alpha. We construct the Stancu-type operators of alpha-bernstein-Schurer-kantorovichoperators. Here the shape parameter alpha is an element of[0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha \in [0,1]$\end{document}. We obtain the convergence of proposed operators in terms of Lipschitz-continuous functions and Peetre's K-functional by using the modulus of continuity of orders one and two.
Inspired by the construction of bernstein and kantorovichoperators, we introduce a family of positive linear operators K n \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}...
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Inspired by the construction of bernstein and kantorovichoperators, we introduce a family of positive linear operators K n \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{K}_n$$\end{document} preserving the affine functions. Their approximation properties are investigated and compared with similar properties of other operators. We determine the central moments of all orders of K n \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {K}}}_n$$\end{document} and use them in order to establish Voronovskaja type formulas. A special attention is paid to the shape preserving properties. The operators K n \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {K}}}_n$$\end{document} preserve monotonicity, convexity, strong convexity and approximate concavity. They have also the property of monotonic convergence under convexity. All the established inequalities involving convex functions can be naturally interpreted in the framework of convex stochastic ordering.
We construct the Stancu variant of bernstein-kantorovich operators based on shape parameter alpha. We investigate the rate of convergence of these operators by means of suitable modulus of continuity to any continuous...
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We construct the Stancu variant of bernstein-kantorovich operators based on shape parameter alpha. We investigate the rate of convergence of these operators by means of suitable modulus of continuity to any continuous functions f(x) on x is an element of and Voronovskaja-type approximation theorem. Moreover, we study other approximation properties of our new operators such as weighted approximation as well as pointwise convergence. Finally, some illustrative graphics are provided here by our new Stancu-type bernstein-kantorovich operators in order to demonstrate the significance of our operators.
In this article, we consider modified bernstein-kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as tha...
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In this article, we consider modified bernstein-kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ones classically used. We obtain a simultaneous approximation result for our operators. Also, we prove two direct approximation results via the usual second-order modulus of smoothness and the second-order Ditzian-Totik modulus of smoothness, respectively. Finally, some graphical illustrations are provided.
In the present paper, we construct a new sequence of bernstein-kantorovich operators depending on a parameter alpha. The uniform convergence of the operators and rate of convergence in local and global sense in terms ...
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In the present paper, we construct a new sequence of bernstein-kantorovich operators depending on a parameter alpha. The uniform convergence of the operators and rate of convergence in local and global sense in terms of first- and second-order modulus of continuity are studied. Some graphs and numerical results presenting the advantages of our construction are obtained. The last section is devoted to bivariate generalization of bernstein-kantorovich operators and their approximation behaviors.
In this manuscript, a new family of (lambda,mu)-bernstein-kantorovich operators are introduced. A Kovovkin type approximation theorem is obtained, the rate of convergence and A-statistical convergence are investigated...
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In this manuscript, a new family of (lambda,mu)-bernstein-kantorovich operators are introduced. A Kovovkin type approximation theorem is obtained, the rate of convergence and A-statistical convergence are investigated by using the modulus of smoothness, Steklov mean and Korovkin-type statistical approximation theorem, graphical representations and numerical examples are also presented to compare the newly defined ones with other forms. Finally, an asymptotic estimate on the rate of convergence for some absolutely continuous functions are derived by using the Bojainc-Cheng decomposition method and some analysis techniques.
We give a solution to a problem posed by Totik at the 1992 Texas conference concerning the strong converse inequality for approximation by bernstein-kantorovich operators. The approximation behaviour of these operator...
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We give a solution to a problem posed by Totik at the 1992 Texas conference concerning the strong converse inequality for approximation by bernstein-kantorovich operators. The approximation behaviour of these operators is characterized for 1 less than or equal to p less than or equal to infinity by using an appropriate K-functional which, for 1 < p less than or equal to infinity, is equivalent to a second order modulus and an extra term. Crucial in our approach are estimates for the derivatives of iterated kantorovichoperators.
. In this paper, we construct a new sequence of Riemann-Liouville type fractional bernstein-kantorovich operators Kn & alpha;(f;x) depending on a parameter & alpha;. We prove a Korovkin type approximation theo...
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. In this paper, we construct a new sequence of Riemann-Liouville type fractional bernstein-kantorovich operators Kn & alpha;(f;x) depending on a parameter & alpha;. We prove a Korovkin type approximation theorem and discuss the rate of convergence with the first and second order modulus of continuity of these operators. Moreover, we introduce a new operator that preserves affine functions from Riemann-Liouville type fractional bernstein-kantorovich operators. Further, we define the bivariate case of Riemann-Liouville type fractional bernstein-kantorovich operators and investigate the order of convergence. Some numerical results are given to illustrate the convergence of these operators and its comparison with the classical case of these operators.
In this paper we will prove the Korovkin type theorem for bernstein-kantorovich type operators via A- statistical convergence and power summability method. Also we give the rate of the convergence related to the above...
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In this paper we will prove the Korovkin type theorem for bernstein-kantorovich type operators via A- statistical convergence and power summability method. Also we give the rate of the convergence related to the above summability methods and in the last sections we give a kind of Voronovskaya type theorem for A- statistical convergence and Gruss-Voronovskaya type theorem.
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