Approximation Properties by Generalized-Baskakov- Kantorovich-Stancu Type Operators

Abstract

In this paper, we introduce generalized Baskakov Kantorovich Stancu type operators and investigate direct result, local approximation and weighted approximation properties of these operators. Modulus of continuity, second modulus of continuity, Peeter's K-functional, weighted modulus of continuity and Lipschitz class are considered to prove our results.

Approximation of Modified Jakimovski-Leviatan-Beta Type Operators

“…In the space [0, ∞), following Gadžiev [9,10,17], we recall the weighted spaces of the functions for which the analogous of the Korovkin theorem holds (see also [1,5,19]) .…”

Some approximation properties of a new class of linear operators

“…The generalized Jain operators as variant of the Lupaş operators were studied by Patel and Mishra . Some related work in this area can be found in other works . Motivated by this, we give further modification of Jain operators in this paper with the help of a generalized Poisson‐type distribution, establish its convergence properties, and discuss its degree of approximation, asymptotic formula, and statistical convergence.…”

“…15 Some related work in this area can be found in other works. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] Motivated by this, we give further modification of Jain operators in this paper with the help of a generalized Poisson-type distribution, establish its convergence properties, and discuss its degree of approximation, asymptotic formula, and statistical convergence. The results for the Szász-Mirakyan operators and Jain operators can be obtained from our operators as a particular case.…”

Simultaneous approximation by Szász–Mirakjan–Stancu–Durrmeyer type operators

“…Acar et al [1], Bardaro and Mantellini [2], Gairola et al [6], López-Moreno [9], Mishra et al [11][12][13][14][15][16][17], Patel and Mishra [18], Sun [21], Wafi et al [23] and many others studied approximation properties of operators given above, their modifications and generalizations. In this paper we study simultaneous approximation of the summation-integral type of modification of the type (1.7) with Stancu (1.3) type terms, which we call Szász-Mirakjan-Stancu-Durrmeyer type operators.…”