Approximation properties of λ‐Bernstein‐Kantorovich operators with shifted knots

Abstract

In the present article, Kantorovich variant of λ‐Bernstein operators with shifted knots are introduced. The advantage of using shifted knot is that one can do approximation on [0,1] as well as on its subinterval. In addition, it adds flexibility to operators for approximation. Some basic results for approximation as well as rate of convergence of the introduced operators are established. The rth order generalization of the operator is also discussed. Further for comparisons, some graphics and error estimation tables are presented using MATLAB.

Convergence of λ-Bernstein operators based on (p, q)-integers

“…In 2019, Cai et al [4] proposed new λ-Bernstein operators based on q-integers and established a statistical approximation theorem. Some other papers also mention λ-Bernstein operators, see [5,6].…”

On new Bézier bases with Schurer polynomials and corresponding results in approximation theory

“…A new type -Bernstein operators have been introduced by Cai et al in [6] based on Bézier bases de…ned by Ye et al in [30]. We refer to [5,6,20,23,26] for recent studies about -Bernstein type operators and [13,14,28] for some Schuer type operators.…”

Bivariate α,q-Bernstein–Kantorovich Operators and GBS Operators of Bivariate α,q-Bernstein–Kantorovich Type

“…As we know, the application of q-integers in approximation theory has been a hot topic in recent decades. Even recently, there have also been many papers mentioned about the q-analogue of Bernstein type operators, such as [4][5][6][7][8][9][10][11][12][13][14].…”