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Inverse approximation and GBS of bivariate Kantorovich type sampling series

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Abstract

In this paper, we derive an inverse result for bivariate Kantorovich type sampling series for \( f \in C^{(2)}({\mathbb {R}}^{2})\) (the space of all continuous functions with upto second order partial derivatives are continuous and bounded on \( {\mathbb {R}}^{2}).\) Further, we introduce the generalized Boolean sum (GBS) operators of bivariate Kantorovich type sampling series. We also study the rate of approximation for the GBS operators in terms of mixed modulus of smoothness and mixed K-functionals for the space of Bögel-continuous functions. Finally, we give some examples for the kernel to which the theory can be applied along with the graphical representations.

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Acknowledgements

The authors are extremely grateful to the reviewer for a careful reading of the manuscript and making valuable suggestions leading to a better presentation of the paper. The second author is thankful to the “Ministry of Human Resource and Development”, India for financial support to carry out his research work. The first author is supported by DST, SERB, India, Project file no: EEQ/2017/000201.

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  1. Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, Nagpur, 440010, India

    A. Sathish Kumar & Bajpeyi Shivam

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  1. A. Sathish Kumar
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Correspondence to Bajpeyi Shivam.

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Kumar, A.S., Shivam, B. Inverse approximation and GBS of bivariate Kantorovich type sampling series. RACSAM 114, 82 (2020). https://doi.org/10.1007/s13398-020-00805-7

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