Approximation of functions by a new family of generalized Bernstein operators

Chen, Xiaoyan; Tan, Jieqing; Zhi, Liu; Xie, Junshan

doi:10.1016/j.jmaa.2016.12.075

Cited by 101 publications

(65 citation statements)

References 12 publications

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“…Since the famous Bernstein polynomial was proposed in 1912, the study of Bernstein type operators has not ceased. In 2017, Chen et al [1] introduced and studied the monotonic, convex properties and also some other important properties of a new generalized positive linear Bernstein operators with parameter α which are defined as…”

Section: Introductionmentioning

confidence: 99%

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

2019

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In this paper, we introduce a family of bivariate α , q -Bernstein–Kantorovich operators and a family of G B S (Generalized Boolean Sum) operators of bivariate α , q -Bernstein–Kantorovich type. For the former, we obtain the estimate of moments and central moments, investigate the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and Peetre’s K-functional. For the latter, we estimate the rate of convergence of these G B S operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness.

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Section: Introductionmentioning

confidence: 99%

“…In the same year, Mohiuddine et al [2] constructed the Kantorovich type of these family of Bernstein operators (1). These operators they introduced are…”

Section: Introductionmentioning

confidence: 99%

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

2019

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“…Among other papers, we refer the readers to [3,7,9,13,23,25]. For f 2 C OE0; 1; Chen et al in [10] introduced a generalization of the Bernstein operators based on a non-negative parameter˛.0 Ä˛Ä 1/ as follows: and n 2: They proved the rate of convergence, Voronovskaja type asymptotic formula and shape preserving properties for these operators. For the special case,˛D 1; these operators reduce the well-known Bernstein operators.…”

Section: Introductionmentioning

confidence: 99%

Blending type approximation by generalized Bernstein-Durrmeyer type operators

Kajla¹,

Acar²

2018

MMN

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“…Recently, Chen et al [20] introduced a new family of α -Bernstein operators, and investigated some approximation properties, such as the rate of convergence, Voronovskaja-type asymptotic formulas, etc. They also obtained the monotonic and convex properties.…”

Section: Introductionmentioning

confidence: 99%

Shape-preserving properties of a new family of generalized Bernstein operators

Cai

2018

J Inequal Appl

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In this paper, we introduce a new family of generalized Bernstein operators based on q integers, called -Bernstein operators, denoted by . We investigate a Kovovkin-type approximation theorem, and obtain the rate of convergence of to any continuous functions f. The main results are the identification of several shape-preserving properties of these operators, including their monotonicity- and convexity-preserving properties with respect to . We also obtain the monotonicity with n and q of .

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Approximation of functions by a new family of generalized Bernstein operators

Cited by 101 publications

References 12 publications

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

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

Blending type approximation by generalized Bernstein-Durrmeyer type operators

Shape-preserving properties of a new family of generalized Bernstein operators

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