Simultaneous approximation by combinations of Bernstein–Kantorovich operators

Li, Cheng; Xie, Li

doi:10.1007/s10474-011-0162-7

Cited by 3 publications

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References 9 publications

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“…The Kantorovich sampling operators defined in Bardaro et al [20] was inspired by the Kantorovich modification of Bernstein polynomials (see Kantorovich [26]). The various direct and inverse approximation results for the Kantorovich type operators were analyzed in previous studies [27–33]. Though we analyze several approximation properties of certain linear and nonlinear operators, but one of the major study in the theory of approximation is studying the rate of convergence of Voronovsakaya type theorem.…”

Section: Introductionmentioning

confidence: 99%

On bivariate Kantorovich exponential sampling series

Kumar

Shivam

2023

Math Methods in App Sciences

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In this paper, we introduce and analyze the approximation properties of bivariate generalization for the family of Kantorovich type exponential sampling series. We derive the basic convergence result and Voronovskaya type theorem for the proposed sampling series. Using logarithmic modulus of smoothness, we establish the quantitative estimate of order of convergence for the Kantorovich type exponential sampling series. Furthermore, we study the convergence results for the generalized Boolean sum (GBS) operator associated with bivariate Kantorovich exponential sampling series. At the end, we provide a few examples of kernels to which the presented theory can be applied along with the graphical representation and error estimates.

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Section: Introductionmentioning

confidence: 99%