Abstract
The purpose of the present paper is to investigate the degree of approximation of the \(\lambda \)-Bernstein operators introduced by Cai et al. (J Inequal Appl 61:1–11, 2018 [9]) by means of the Steklov mean, the Ditizian–Totik modulus of smoothness and the approximation of functions with derivatives of bounded variation. We introduce the bivariate case of the above operators and investigate the rate of convergence with the aid of the total and partial modulus of continuity and the Peetre’s K-functional. Furthermore, we define the associated GBS (Generalized Boolean Sum) operator of the bivariate operators and establish the degree of approximation in terms of the mixed modulus of smoothness for Bögel continuous and Bögel differentiable functions.
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Acknowledgements
The first author is thankful to the “Ministry of Human Resource and Development”, New Delhi, India for financial support to carry out the above work.
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Chauhan, R., Agrawal, P.N. (2020). Degree of Approximation by Generalized Boolean Sum of \(\lambda \)-Bernstein Operators. In: Deo, N., Gupta, V., Acu, A., Agrawal, P. (eds) Mathematical Analysis I: Approximation Theory . ICRAPAM 2018. Springer Proceedings in Mathematics & Statistics, vol 306. Springer, Singapore. https://doi.org/10.1007/978-981-15-1153-0_9
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DOI: https://doi.org/10.1007/978-981-15-1153-0_9
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