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

Abstract

A new type Bézier bases with shape parameters have been de-…ned [30, Ye et al., 2010]. We slightly modify these bases to establish new Bézier bases with Schurer polynomials and shape parameters. We construct a new type Schurer operators via de…ned new Bézier-Schurer bases. Also, we study statistical convergence properties of these operators and obtain an estimate for the rate of weighted A-statistical convergence. Moreover, we prove two Voronovskaja-type theorems including a Voronovskaja-type approximation theorem using weighted A-statistical convergence.

Note on a New Construction of Kantorovich Form q-Bernstein Operators Related to Shape Parameter λ

“…In the year 2020, Mursaleen et al [21] considered Chlodowsky kind (λ, q)-Bernstein-Stancu polynomials and derived Korovkin-type convergence, and Voronovskaya-type asymptotic theorems. For some recent relevant works we refer to [22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Approximation by Szasz-Mirakjan-Baskakov operators based on shape parameter

“…They obtained several theorems such as Korovkin type approximation, local approximation, Lipschitz type convergence, Voronovskaja and Grüss-Voronovskaja type for the operators (4). We can mention some recent works based on shape parameter λ ∈ [−1, 1], see: [8,9,6,7,29,30,20,21,3,28,18,22,23,24,25].…”

A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices

“…Using certain types of statistical convergences instead of usual convergence in Korovkin type approximation theory provides several benefits. The statistical convergence extends the scope of classical convergence of sequences of numbers or functions, and it has been used in various fields of mathematics such as summability theory [13], topology [14], optimization [15], measure theory [16], number theory [17], trigonometric series [18], approximation by positive linear operators [9,[19][20][21][22][23][24][25]. Statistical convergence of double and single sequences were given in [26][27][28].…”