A General Korovkin Result Under Generalized Convergence

Pedro GARRANCHO

doi:https://doi.org/10.33205/cma.530987

Article Details

A General Korovkin Result Under Generalized Convergence

Authors:

Pedro GARRANCHO

Publisher:

Tuncer ACAR

Main Topics:

Mathematics

Journal:

Constructive Mathematical Analysis 2019 Vol.2 Issue 2, pp.81-88

Document Type:

Article

Publication Date:

5/2019

Document Language:

English

Document ID (Org No.):

2000914222

Frequency:

Quarterly

pISSN:

2651-2939

DOI:

https://doi.org/10.33205/cma.530987

Abstract:

 


In this paper the classic result of Korovkin about the convergence of sequences of functions defined from sequences of linear operators is reformulated in terms of generalized convergence. This convergence extends some others given in the literature. The operator of the sequence fulfill a shape preserving property more general than the positivity. This property is related with certain extension of the notion of derivative. This extended derivative is precisely the object of the approximation process. The study is completed by analysing the conditions for the existence of an asymptotic formula, from which some interesting consequences are derived as a local version of the shape preserving property. Finally, as applications of the previous results, the author use the following notion of generalized convergence, an extension of Nörlund-Cesaro summability given by V. Loku and N. L. Braha in 2017. A way to transfer a notion of generalized convergence to approximation theory by means of linear operators is showed.

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Article Details

A General Korovkin Result Under Generalized Convergence

Authors: Pedro GARRANCHO

Publisher: Tuncer ACAR

Main Topics: Mathematics

Journal: Constructive Mathematical Analysis 2019 Vol.2 Issue 2, pp.81-88

Document Type: Article

Publication Date: 5/2019

Document Language: English

Document ID (Org No.): 2000914222

Frequency: Quarterly

pISSN: 2651-2939

DOI: https://doi.org/10.33205/cma.530987

Issues

Authors:

Pedro GARRANCHO

Publisher:

Tuncer ACAR

Main Topics:

Mathematics

Journal:

Constructive Mathematical Analysis 2019 Vol.2 Issue 2, pp.81-88

Document Type:

Article

Publication Date:

5/2019

Document Language:

English

Document ID (Org No.):

2000914222

Frequency:

Quarterly

pISSN:

2651-2939

DOI:

https://doi.org/10.33205/cma.530987