, Volume 64, Issue 1, pp 1–23 | Cite as

q- Lupas Kantorovich operators based on Polya distribution

  • P. N. Agrawal
  • Pooja Gupta


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.


Degree of approximation Modulus of continuity A-statistical convergence Peetre‘s K-functional 

Mathematics Subject Classification

26A15 41A25 41A36 



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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© Università degli Studi di Ferrara 2017

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia

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