# Approximation by generalized bivariate Kantorovich sampling type series

Approximation by generalized bivariate Kantorovich sampling type series The purpose of this paper is to construct a bivariate generalization of new family of Kantorovich type sampling operators $$(K_w^{\varphi }f)_{w>0}.$$ ( K w φ f ) w > 0 . First, we give the pointwise convergence theorem and a Voronovskaja type theorem for these Kantorovich generalized sampling series. Further, we obtain the degree of approximation by means of modulus of continuity and quantitative version of Voronovskaja type theorem for the family $$(K_w^{\varphi }f)_{w>0}.$$ ( K w φ f ) w > 0 . Finally, we give some examples of kernels such as box spline kernels and Bochner–Riesz kernel to which the theory can be applied. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

# Approximation by generalized bivariate Kantorovich sampling type series

, Volume 27 (2) – May 24, 2018
21 pages

/lp/springer-journals/approximation-by-generalized-bivariate-kantorovich-sampling-type-994HjN0rQX
Publisher
Springer Journals
Subject
Mathematics; Analysis; Functional Analysis; Abstract Harmonic Analysis; Special Functions; Fourier Analysis; Measure and Integration
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-018-0085-6
Publisher site
See Article on Publisher Site

### Abstract

The purpose of this paper is to construct a bivariate generalization of new family of Kantorovich type sampling operators $$(K_w^{\varphi }f)_{w>0}.$$ ( K w φ f ) w > 0 . First, we give the pointwise convergence theorem and a Voronovskaja type theorem for these Kantorovich generalized sampling series. Further, we obtain the degree of approximation by means of modulus of continuity and quantitative version of Voronovskaja type theorem for the family $$(K_w^{\varphi }f)_{w>0}.$$ ( K w φ f ) w > 0 . Finally, we give some examples of kernels such as box spline kernels and Bochner–Riesz kernel to which the theory can be applied.

### Journal

The Journal of AnalysisSpringer Journals

Published: May 24, 2018

### References

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