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q- Lupas Kantorovich operators based on Polya distribution

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Abstract

The purpose of the present paper is to introduce a Kantorovich modification of the q-analogue of the Stancu operators defined by Nowak (J Math Anal Appl 350:50–55, 2009). We study a local and a direct approximation theorem by means of the Ditzian–Totik modulus of smoothness. Further A-statistical convergence properties of these operators are investigated. Next, a bivariate generalization of these operators is introduced and its rate of convergence is discussed with the aid of the partial and complete modulus of continuity and the Peetre‘s K-functional.

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Acknowledgements

The second 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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  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    P. N. Agrawal & Pooja Gupta

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  1. P. N. Agrawal
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  2. Pooja Gupta
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Correspondence to P. N. Agrawal.

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Agrawal, P.N., Gupta, P. q- Lupas Kantorovich operators based on Polya distribution. Ann Univ Ferrara 64, 1–23 (2018). https://doi.org/10.1007/s11565-017-0291-1

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