Some approximation results on a class of new type λ-Bernstein polynomials

Abstract

The main concern of this article is to acquire some approximation properties of a new class of Bernstein polynomials based on Bézier basis functions with shape parameter λ ∈ [−1,1] . We prove Korovkin type approximation theorem and estimate the degree of convergence in terms of the modulus of continuity, for the functions belong to Lipschitz type class and Peetre's K -functional, respectively. Additionally, with the help of Maple software, we present the comparison of the convergence of newly defined operators to the certain functions with some graphical illustrations and error estimation tables. Also, we conclude that the error estimation of our newly defined operators in some cases is better than classical Bernstein operators [3], Cai et al. [4] and Izgi [10].

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].…”

Enhanced Approximation Techniques: Stancu-type (λ,μ)-Bernstein-Kantorovich Operators

“…Yadav et al [12] considered a modiőcation of α-Bernstein summation-integral type operators in view of a strictly positive continuous function. Aslan et al [13] proposed and studied a novel family of λ-Bernstein operators. Cai et al [14] invented a novel of (λ, q)-Bernstein operators.…”

On One- and Two-Dimensional α–Stancu–Schurer–Kantorovich Operators and Their Approximation Properties

“…In [13], the authors investigated various pointwise and uniform approximation results. Furthermore, many researchers, e.g., Kilicman et al [15], Acar et al [16], Aral et al [17], Cai et al [18,19], Çetin et al [20,21], Mohiuddine et al [22], Aslan et al [23,24], Acu et al [25], Agrawal [26], Nasiruzzaman et al [27], and Ayman-Mursaleen et al [28,29], have intensively studied α-Bernstein operators and their modifications for better approximation results. In [30][31][32] some interesting studies have been carried out.…”