Local Smoothness of Functions and Baskakov–Durrmeyer Operators

Song, Li

doi:10.1006/jath.1996.3016

Cited by 6 publications

(3 citation statements)

References 9 publications

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“…In this paper we give relation between local smoothness of function f and local convergence of Szász-Durrmeyer operators M ν n . Results of this type for Berenstain-Durrmeyer operators have been given by Ding-Xuan Zhou [6] and Song Li [3]. By K i (a, b) or K i (a, b, c), i ∈ N * we denote suitable positive constants depending only on indicated parameters.…”

Section: Introductionmentioning

confidence: 99%

Inverse theorem for the Szász-Durrmeyer operators

Świderski

2009

J. Numer. Anal. Approx. Theory

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Section: Introductionmentioning

confidence: 99%

Inverse theorem for the Szász-Durrmeyer operators

Świderski

2009

J. Numer. Anal. Approx. Theory

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“…They have been studied intensively in connection with different branches of analysis such as convex and numerical analysis. We refer the reader to P. Gupta and V. Gupta [9], V. Gupta [10], N. Ispir and C. Atakut [1], [18], V. Gupta, V. Vasishtha and M. K. Gupta [13], G. Feng [7], [8], A. Ciupa [5], N. Ispir [17], S. Li [21], X. Linsen and Z. Xiaoping [22]. Their results improve other related results in literature.…”

Section: Introductionmentioning

confidence: 99%

On a class of Szász-Mirakyan type operators

Walczak

2008

Czech Math J

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“…Note that some local smoothness theorems for the Baskakov-Durrmeyer operators may be found in [22]. Theorem 3.3.…”

Section: Combining (22)-(24) We Havementioning

confidence: 99%

On integral type generalizations of positive linear operators

Duman

Özarslan²,

Doğru

2006

Studia Math.

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Abstract. We introduce a sequence of positive linear operators including many integral type generalizations of well known operators. Using the concept of statistical convergence we obtain some Korovkin type approximation theorems for those operators, and compute the rates of statistical convergence. Furthermore, we deal with the local approximation and the rth order generalization of our operators.1. Introduction. In this paper, we are concerned with Korovkin type theorems for a general sequence of positive linear operators including many integral type generalizations of well known operators in approximation theory via the concept of statistical convergence. The study of Korovkin type approximation is a well established area of research, which deals with the problem of approximating a function f by means of a sequence of positive linear operators L n (f ). Statistical convergence, though introduced over fifty years ago, has only recently become an area of active research. In particular, it has made an appearance in approximation theory [14] (see also [6]-[8]).The first section of this paper collects some basic ideas related to statistical convergence and introduces a sequence of positive linear operators which generates many Durrmeyer type and Kantorovich type generalizations of well known operators while the second section gives a Korovkin type approximation theorem for these operators on an appropriate weighted space. The third section addresses some problems concerning rates of statistical convergence by means of the modulus of continuity and elements of the Lipschitz class. This section also includes a study of local smoothness of these operators. In the last section, we deal with the approximation properties of the rth order generalization of our operators.We now introduce some notation and basic definitions used in this paper.

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Local Smoothness of Functions and Baskakov–Durrmeyer Operators

Cited by 6 publications

References 9 publications

Inverse theorem for the Szász-Durrmeyer operators

Inverse theorem for the Szász-Durrmeyer operators

On a class of Szász-Mirakyan type operators

On integral type generalizations of positive linear operators

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