Statistically Relatively Uniform Convergence of Positive Linear Operators

Demirci, Kami̇l; Orhan, Sevda

doi:10.1007/s00025-015-0484-9

Cited by 33 publications

(18 citation statements)

References 13 publications

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“…Later on, Chittenden [10] gave a detailed definition of this convergence (which is equivalent to Moore's definition). Recently, Demirci and Orhan [11] defined a new type of statistical convergence by using this convergence and they presented its applications to Korovkin type approximation. For more details on these types of convergences and their applications, we refer to [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Statistical relative uniform convergence of a double sequence of functions at a point and applications to approximation theory

Yıldız

2021

Cumhuriyet Science Journal

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In the present paper, we introduce a new kind of convergence, called the statistical relative uniform convergence, for a double sequence of functions at a point, where the relative uniform convergence of the set of the neighborhoods of the given point is considered. By the use of the statistical relative uniform convergence, we investigate a Korovkin type approximation theorem which makes the proposed method stronger than the ones studied before. After that, we give an example using this new type of convergence. We also study the rate of convergence of the proposed convergence.

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Section: Introductionmentioning

confidence: 99%

Statistical relative uniform convergence of a double sequence of functions at a point and applications to approximation theory

Yıldız

2021

Cumhuriyet Science Journal

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“…There have been also several studies on Korovkin-type theorems related to convergence associated with summability methods, statistical and filter convergence (see e.g., [5,8,9,29,[32][33][34]49]).…”

Section: Introductionmentioning

confidence: 99%

Abstract Korovkin-type theorems in the filter setting with respect to relative uniform convergence

Boccuto¹,

Demirci²,

Yıldız³

2020

Turk J Math

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“…Recalling this concept, a sequence of functions (f n ) defined over [a, b] Thus, uniform convergence can be viewed as a special case of relative uniform convergence (or, convergent uniformly relative to a non-zero scale function). Recently, Demirci and Orhan [16] defined the notion of relatively uniform statistical convergence of a sequence of functions which is based on the natural density of a set as follows:…”

Section: Introductionmentioning

confidence: 99%

A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

Paikray¹,

Parida²,

Mohiuddine³

2020

Eur. J. Pure Appl. Math.

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The aim of this paper is to introduce the notions of relatively deferred Nörlund uniform statistical convergence as well as relatively deferred Norlund point-wise statistical convergence through the dierence operator of fractional order of fuzzy-number-valued sequence of functions, and a type of convergence which lies between aforesaid notions, namely, relatively deferred Nörlund equi-statistical convergence. Also, we investigate the inclusion relations among these aforesaidnotions. As an application point of view, we establish a fuzzy approximation (Korovkin-type) theorem by using our new notion of relatively deferred Norlund equi-statistical convergence and intimate that this result is a non-trivial generalization of several well-established fuzzy Korovkin-type theorems which were presented in earlier works. Moreover, we estimate the fuzzy rate of the relatively deferred Nörlund equi-statistical convergence involving a non-zero scale function by using the fuzzy modulus of continuity.

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Statistically Relatively Uniform Convergence of Positive Linear Operators

Cited by 33 publications

References 13 publications

Statistical relative uniform convergence of a double sequence of functions at a point and applications to approximation theory

Statistical relative uniform convergence of a double sequence of functions at a point and applications to approximation theory

Abstract Korovkin-type theorems in the filter setting with respect to relative uniform convergence

A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

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