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Integral-type generalizations of operators obtained from certain multivariate polynomials. (English) Zbl 1142.41005

For the Kantorovich-type generalizations of the positive linear operators obtained from the Chan-Chyan-Srivastava multivariable polynomials [W.-C. C. Chan, C.-J. Chyan and H. M. Srivastava, Integral Transforms Spec. Funct. 12, No. 2, 139–148 (2001; Zbl 1057.33003)], the authors establish approximation theorems including a statistical Korovkin-type result and rates of A-statistical convergence with the aid of the modulus of continuity, Lipschitz class functionals and Peetre \(K\)-functionals.

MSC:

41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Citations:

Zbl 1057.33003
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References:

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