Approximation for a generalization of Bernstein operators

Abstract In this paper, we give a direct approximation theorem, inverse theorem, and equivalent theorem for a generalization of Bernstein operators in the space L p [ 0 , 1 ] $L_{p}[0,1]$ ( 1 ≤ p ≤ ∞ $1\leq p \leq\infty$ ).

Bibliographic Details
Main Authors:	Guofen Liu, Xiuzhong Yang
Format:	Article
Language:	English
Published:	SpringerOpen 2016-08-01
Series:	Journal of Inequalities and Applications
Subjects:	generalized Bernstein-Kantorovich operators modulus of smoothness K-functional equivalent approximation theorem
Online Access:	http://link.springer.com/article/10.1186/s13660-016-1147-4

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spelling	doaj-372dee1e29414ff28f07bff403a9ebdf2020-11-25T01:13:24ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-08-012016111010.1186/s13660-016-1147-4Approximation for a generalization of Bernstein operatorsGuofen Liu0Xiuzhong Yang1College of Mathematics and Information Science, Hebei Normal UniversityCollege of Mathematics and Information Science, Hebei Normal UniversityAbstract In this paper, we give a direct approximation theorem, inverse theorem, and equivalent theorem for a generalization of Bernstein operators in the space L p [ 0 , 1 ] $L_{p}[0,1]$ ( 1 ≤ p ≤ ∞ $1\leq p \leq\infty$ ).http://link.springer.com/article/10.1186/s13660-016-1147-4generalized Bernstein-Kantorovich operatorsmodulus of smoothnessK-functionalequivalent approximation theorem
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Guofen Liu Xiuzhong Yang
spellingShingle	Guofen Liu Xiuzhong Yang Approximation for a generalization of Bernstein operators Journal of Inequalities and Applications generalized Bernstein-Kantorovich operators modulus of smoothness K-functional equivalent approximation theorem
author_facet	Guofen Liu Xiuzhong Yang
author_sort	Guofen Liu
title	Approximation for a generalization of Bernstein operators
title_short	Approximation for a generalization of Bernstein operators
title_full	Approximation for a generalization of Bernstein operators
title_fullStr	Approximation for a generalization of Bernstein operators
title_full_unstemmed	Approximation for a generalization of Bernstein operators
title_sort	approximation for a generalization of bernstein operators
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2016-08-01
description	Abstract In this paper, we give a direct approximation theorem, inverse theorem, and equivalent theorem for a generalization of Bernstein operators in the space L p [ 0 , 1 ] $L_{p}[0,1]$ ( 1 ≤ p ≤ ∞ $1\leq p \leq\infty$ ).
topic	generalized Bernstein-Kantorovich operators modulus of smoothness K-functional equivalent approximation theorem
url	http://link.springer.com/article/10.1186/s13660-016-1147-4
work_keys_str_mv	AT guofenliu approximationforageneralizationofbernsteinoperators AT xiuzhongyang approximationforageneralizationofbernsteinoperators
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Approximation for a generalization of Bernstein operators

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