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1

Approximation properties of Kantorovich type q-Balázs-Szabados operators

Özkan Esma Yıldız

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

10--19

EN

In this paper, we introduce a new kind of q-Balázs-Szabados-Kantorovich operators called q-BSK operators. We give a weighted statistical approximation theorem and the rate of convergence of the q-BSK operators. Also, we investigate the local approximation results. Further, we give some comparisons associated with the convergence of q-BSK operators.

2

Rate of convergence for Ibragimov-Gadjiev-Durrmeyer operators

Acar T.

Demonstratio Mathematica

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2017

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Vol. 50, nr 1

119--129

EN

The present paper deals with the rate of convergence of the general class of Durrmeyer operators, which are generalization of Ibragimov-Gadjiev operators. The special cases of the operators include some well known operators as particular cases viz. Szász-Mirakyan-Durrmeyer operators, Baskakov-Durrmeyer operators. Here we estimate the rate of convergence of Ibragimov-Gadjiev-Durrmeyer operators for functions having derivatives of bounded variation.

3

On generalized Baskakov-Durrmeyer-Stancu type operators

Kumar A. S., Finta Z., Agrawal P. N.

Demonstratio Mathematica

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2017

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Vol. 50, nr 1

144--155

EN

In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.

4

The impact of the Dirichlet boundary conditions on the convergence of the discretized system of nonlinear equations for potential problems

Kucwaj J.

Computer Assisted Methods in Engineering and Science

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2016

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Vol. 23, no. 1

69--81

EN

The purpose of this paper is the analysis of numerical approaches obtained by describing the Dirichlet boundary conditions on different connected components of the computational domain boundary for potential flow, provided that the domain is a rectangle. The considered problem is a potential flow around an airfoil profile. It is shown that in the case of a rectangular computational domain with two sides perpendicular to the speed direction, the potential function is constant on the connected components of these sides. This allows to state the Dirichlet conditions on the considered parts of the boundary instead of the potential jump on the slice connecting the trail edge with the external boundary. Furthermore, the adaptive remeshing method is applied to the solution of the considered problem.

5

Rate of convergence for certain mixed family of linear positive operators

Maheshwari P., Sharma D.

Journal of Mathematics and Applications

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2010

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Vol. 33

73-78

EN

The present paper deals with the mixed integrated operators Mn(f; x); which are linear and positive having different basis functions in summation and integration respectively. We estimate the rate of convergence for these operators for functions which have derivatives of bounded variation.

6

A direct and accurate adaptive semi-Lagrangian scheme for the Vlasov-Poisson equation

Campos Pinto M. M.

International Journal of Applied Mathematics and Computer Science

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2007

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Vol. 17, no 3

351-359

EN

This article aims at giving a simplified presentation of a new adaptive semi-Lagrangian scheme for solving the (1 + 1)- dimensional Vlasov-Poisson system, which was developed in 2005 with Michel Mehrenberger and first described in (Campos Pinto and Mehrenberger, 2007). The main steps of the analysis are also given, which yield the first error estimate for an adaptive scheme in the context of the Vlasov equation. This article focuses on a key feature of our method, which is a new algorithm to transport multiscale meshes along a smooth flow, in a way that can be said optimal in the sense that it satisfies both accuracy and complexity estimates which are likely to lead to optimal convergence rates for the whole numerical scheme. From the regularity analysis of the numerical solution and how it gets transported by the numerical flow, it is shown that the accuracy of our scheme is monitored by a prescribed tolerance parameter \epsilon which represents the local interpolation error at each time step. As a consequence, the numerical solutions are proved to converge in L\infty towards the exact ones as \epsilon and \delta t tend to zero, and in addition to the numerical tests presented in (Campos Pinto and Mehrenberger, 2007), some complexity bounds are established which are likely to prove the optimality of the meshes.

7

The rate of convergence by a new type of Meyer-König and Zeller operators

Gupta V., Abel U.

Fasciculi Mathematici

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2004

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Nr 34

15-23

EN

In the present paper we introduce a simple integral modification of Meyer-Konig and Zeller operators and study their rate of convergence, for functions of bounded variation.

8

Ergodic theorems for Markov chains represented by iterated function systems

Stenflo O.

Bulletin of the Polish Academy of Sciences. Mathematics

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2001

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Vol. 49, no 1

27-43

EN

We consider Markov chains represented in the form Xn+1 = f (Xn, In), where {In} is a sequence of independent, identically distributed (i.i.d.) random variables, and where f is a measurable function. Any Markov chain {Xn} on a Polish state space may be represented in this form i.e. can be considered as arising from an iterated function system (IFS). A distributional ergodic theorem, including rates of convergence in the Kantorovich distance is proved for Markov chains under the condition that an IFS representation is "stochastically contractive" and "stochastically bounded". We apply this result to prove our main theorem giving upper bounds for distances between invariant probability measures for iterated function systems. We also give some examples indicating how ergodic theorems for Markov chains may be proved by finding contractive IFS representations. These ideas are applied to some Markov chains arising from iterated function systems with place dependent probabilities.