Approximation by Stancu–Chlodowsky type λ-Bernstein operators

Abstract

<jats:title>Abstract</jats:title><jats:p>In this paper, we give some approximation properties by Stancu–Chlodowsky type λ-Bernstein operators in the polynomial weighted space and obtain the convergence properties of these operators by using Korovkin’s theorem. We also establish the direct result and the Voronovskaja type asymptotic formula.</jats:p>

Approximation by Riemann–Liouville type fractional α$$ \alpha $$‐Bernstein–Kantorovich operators

“…The magnificent polynomials of Bernstein were likewise used in many different mathematical fields for the purpose of solving partial differential equations numerically, computer-aided geometric design (CAGD), computer graphics, and so on. For more information, readers are referred to the literature [30][31][32][33][34][35][36].…”

Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\lambda$

“…For the operators defined by (4), they studied some theorems such as Korovkin type convergence, local approximation, Lipschitz type convergence, Voronovskaja and Grüss-Voronovskaja type. Also, we refer some recent works based on shape parameter λ ∈ [−1, 1], see details: [5,6,8,[19][20][21][22][23][24][26][27][28].…”

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].…”