Approximation Strategy by Positive Linear Operators

Xiao, Wei

doi:10.1155/2013/856084

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Introduction and Basic Definitions1

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2022

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“…To deal with the approximation in L p [0, 1] (1 ≤ p < ∞) for which Bernstein operators are unsuitable, Bernstein-Kantorovich operators [12] and Bernstein-Durrmeyer operators [6] were introduced. Jackson type estimation by Kantorovich type positive linear operators in L p -spaces is studied in [28] while weighted L p -approximation was studied in [7].…”

Section: Introduction and Basic Definitionsmentioning

confidence: 99%

Approximation by q-Bernstein-Stancu-Kantorovich operators with shifted knots of real parameters

Mursaleen

Kılıçman

Nasiruzzaman

2022

Filomat

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Our main purpose of this article is to study the convergence and other related properties of q-Bernstein-Kantorovich operators including the shifted knots of real positive numbers. We design the shifted knots of Bernstein-Kantorovich operators generated by the basic q-calculus. More precisely, we study the convergence properties of our new operators in the space of continuous functions and Lebesgue space. We obtain the degree of convergence with the help of modulus of continuity and integral modulus of continuity. Furthermore, we establish the quantitative estimates of Voronovskaja-type.

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Section: Introduction and Basic Definitionsmentioning

confidence: 99%