Approximation by generalized bivariate Kantorovich sampling type series

Kumar, A. Sathish; Devaraj, P.

doi:10.1007/s41478-018-0085-6

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2020

2023

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Cited by 9 publications

(3 citation statements)

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“…Corollary 3.1 Let χ be the kernel and f ∈ C (1) (R + ). Then, we have the following asymptotic formula…”

Section: Approximation Resultsmentioning

confidence: 99%

See 1 more Smart Citation

On Approximation by Kantorovich Exponential Sampling Operators

Bajpeyi

Kumar

2021

Numerical Functional Analysis and Optimization

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In this article, we extend our study of Kantorovich type exponential sampling operators introduced in [34]. We derive the Voronovskaya type theorem and its quantitative estimates for these operators in terms of an appropriate K-functional. Further, we improve the order of approximation by using the convex type linear combinations of these operators. Subsequently, we prove the estimates concerning the order of convergence for these linear combinations. Finally, we give some examples of kernels along with the graphical representations.

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“…Corollary 3.1 Let χ be the kernel and f ∈ C (1) (R + ). Then, we have the following asymptotic formula…”

Section: Approximation Resultsmentioning

confidence: 99%

“…In the last few decades, the Kantorovich modifications of several operators have been constructed and analyzed, eg. [5,7,9,25,29,31,36,35,1,33,2]. We also refer some of the recent developments related to the theory of exponential sampling, see [16,12,17,3,18,34].…”

Section: Introductionmentioning

confidence: 99%

On Approximation by Kantorovich Exponential Sampling Operators

Bajpeyi

Kumar

2021

Numerical Functional Analysis and Optimization

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“…From a theoretical point of view, these operators were also studied in [24,28,29,35,34] and they can be considered as a semi-discrete operator defined by two kernel functions ϕ and ψ, the second one generating the integral mean. Thus, in order to obtain a general and unifying theory, one can think to replace the integral mean by an arbitrary convolution integral operator generated by a suitable kernel.…”

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confidence: 99%