On the integrated Baskakov type operators

Exponential moments and simultaneous approximation properties for Durrmeyer type operators with weights of Szasz basis functions

“…In particular, for the Sász operators we have α 1 = α 2 = a = b = 0 but in order to consider later higher order derivatives we will let b ≥ 0 and then formulas (7) and ( 8) simplify to…”

“…1. On the one hand, in (7), the first factor of the expression can be easily bounded by K b+1 −a,β−a , for n ≥ β−a+1. If we also have n > (1 + α 1 x)β − a, for the second factor, as log z ≤ z − 1, for any z ∈ R + , we have…”

On the Rate of Convergence by Generalized Baskakov Operators

“…And when = 1, the operators (8) are (7), while the operators (9) can be represented by [12] , ( ; , ) =…”

“…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].…”

On Rate of Approximation by Modified Beta Operators

“…Very recently Gupta and Agrawal 3 and Gupta et al 4 have obtained an interesting result on the rate of convergence of certain Durrmeyer type operators in ordinary and simultaneous approximation.İspir et al 5 estimated similar results for Kantorovich operators for functions with derivatives of bounded variation. We now extend the study for the modified Beta operators and estimate the rate of convergence of the operators 1 for functions having derivatives of bounded variation.…”