Estimation of Approximation with Jacobi Weights by Multivariate Baskakov Operator

Abstract

We first give the unboundedness of multivariate Baskakov operators with the normal weighted norm. By introducing new norms, using the multivariate decomposition technique and the modulus of smoothness with Jacobi weight, the upper bound estimation of multivariate Baskakov operators is obtained. The obtained results not only generalize the corresponding ones for multivariate Baskakov operators without weights, but also give the approximation accuracy with the Jacobi weights approximation.

Weighted Simultaneous Approximation of the Linear Combinations of Baskakov Operators

“…e Baskakov operator has been studied in many research studies by using a lot of deep methods [9][10][11][12][13]. In previous work [14,15], some pointwise results of the Baskakov operator with weighted approximate were obtained.…”

On the Rate of Convergence by Generalized Baskakov Operators

“…Based on the Baskakov operators, many Baskakov-type operators [2][3][4][5][6][7][8][9][10][11][12][13] and their multivariate Baskakov operators [11,[14][15][16][17][18] were discussed. Particularly, Gupta and Agarwal studied the Baskakov-Kantorovich operators, Szász-Baskakov operators, and so forth in their recent book [6].…”