Results 141 to 150 of about 336 (167)
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Kantorovich Operators of Order k
Numerical Functional Analysis and Optimization, 2011This article is concerned with the k-th order Kantorovich modification of the classical Bernstein operators B n , namely, , where D k f is the derivative of order k and I k f is an antiderivative of order k of the function f. These operators are most useful in simultaneous approximation.
Gonska, Heiner +2 more
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On Kantorovich-Stieltjes operators
Approximation Theory and its Applications, 1993Summary: Let \(\nu\) be a finite Borel measure on \([0,1]\). The Kantorovich-Stieltjes polynomials are defined by \[ K_ n\nu= (n+1) \sum_{k=0}^ n \biggl( \int_{I_{k,n}}d\nu \biggr) N_{k,n} \qquad (n\in\mathbb{N}), \] where \(N_{k,n}(x)= {n \choose k} x^ k(1-x)^{n-k}\) (\(x\in[0,1]\), \(k=1,2,\dots,n\)) are the basic Bernstein polynomials and \(I_{k,n}:=
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Kantorovich‐Type Sampling Operators and Approximation
Mathematical Methods in the Applied SciencesABSTRACTIn this article, we investigate the convergence behavior of generalized sampling operators of Kantorovich‐type. By combining the generalized sampling operators and Kantorovich sampling operators, we obtain the new composition operators and estimate the order of approximation. Then, we establish quantitative estimates for convergence in terms of
Vijay Gupta, Vaibhav Sharma
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Rate of approximation for the Balazs–Kantorovich–Bézier operators
Applied Mathematics and Computation, 2008For a certain class of bounded functions \(f\) defined on the interval \([0,\infty )\), the Balazs-Kantorovich-Bézier operators \(L_{n,\alpha}(f,x),\) \(\alpha \geq 1\) are considered. These operators are represented with the help of suitably chosen positive numbers \(a_n\), depending on \(a_n\) and a parameter \(\alpha\) and some rational functions ...
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Approximation by Lupaṣ–Kantorovich Operators
2018The present article deals with the approximation properties of certain Lupaṣ-Kantorovich operators preserving e−x. We obtain uniform convergence estimates which also include an asymptotic formula in quantitative sense. In the end, we provide the estimates for another modification of such operators, which preserve the function e−2x.
Vijay Gupta +2 more
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Higher-Order Bernstein–Kantorovich Operators
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2023null Anjali, Vijay Gupta
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ψ-Baskakov-Kantorovich Operators
In this paper, we introduce a new family of Baskakov-Kantorovich operators that depend on a function ψ . We compare these new ψ -Baskakov-Kantorovich operators with the classical Baskakov-Kantorovich operators to evaluate their approximation results. Our analysisHUSEYIN AKTUGLU +2 more
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Bernstein-Kantorovich operators on a simplex
Approximation Theory and its Applications, 1995Summary: We give the strong direct theorem and inverse theorem of weak type for multidimensional Kantorovich operators on simplexes.
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Saturation of Kantorovich type operators
Periodica Mathematica Hungarica, 1985The author proves that an integrable function f can be approximated by the Kantorovich type modification of the Szász-Mirakjan and Baskakov operators in the \(L^ 1\) metric in the optimal order \(\{n^{-1}\}\) if and only if \(\phi^ 2f'\) is of bounded variation where \(\phi (x)=x^{1/2}\) and \(\phi (x)=[x(1+x)]^{1/2},\) respectively.
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(?, ?)-Bernstein-Kantorovich operators
In this article, we introduce a new family of ( lambda , psi ) \left(\lambda ,\psi ) -Bernstein-Kantorovich operators which depends on a parameter lambda \lambda , derived from the basis functions of B & eacute;zier curves and an integrable function psi \psi . In this approach, all moments and central moments of the new operators can be obtained inAktuglu, Huseyin +3 more
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