Abstract
In this paper, we introduce the Kantorovich variant of Lupas operators based on Polya distribution with shifted knots. The advantage of using shifted knots is that one can do approximation on [0,1] as well as on its subinterval. Also, it adds flexibility to operators for approximation. First, some basic results for convergence of the introduced operators are established and its rate of convergence is discussed with the aid of the modulus of continuity and Peetre K-functional. Further, a Voronovskaja type theorem for the said operators are studied. Next, a bivariate generalization of these operators are introduced. Some numerical examples with illustrative graphics have been added to justify the theoretical results and also compare the rate of convergence with the help of MATLAB. It has been shown that for suitable choices of parameters error estimate and elapsed time can be further minimized.
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