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

Sevda Yıldız

doi:10.17776/csj.831339

EN

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

Abstract

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.

Keywords

Double sequence, Korovkin theorem, rate of convergence, statistical relative uniform convergence

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Sevda Yıldız ^*
0000-0002-4730-2271
Türkiye

Publication Date

March 29, 2021

Submission Date

November 25, 2020

Acceptance Date

March 3, 2021

Published in Issue

Year 2021 Volume: 42 Number: 1

DOI

https://doi.org/10.17776/csj.831339

IZ

https://izlik.org/JA92HB77TN

APA

Yıldız, S. (2021). Statistical relative uniform convergence of a double sequence of functions at a point and applications to approximation theory. Cumhuriyet Science Journal, 42(1), 123-131. https://doi.org/10.17776/csj.831339

AMA

1.Yıldız S. Statistical relative uniform convergence of a double sequence of functions at a point and applications to approximation theory. CSJ. 2021;42(1):123-131. doi:10.17776/csj.831339

Chicago

Yıldız, Sevda. 2021. “Statistical Relative Uniform Convergence of a Double Sequence of Functions at a Point and Applications to Approximation Theory”. Cumhuriyet Science Journal 42 (1): 123-31. https://doi.org/10.17776/csj.831339.

EndNote

Yıldız S (March 1, 2021) Statistical relative uniform convergence of a double sequence of functions at a point and applications to approximation theory. Cumhuriyet Science Journal 42 1 123–131.

IEEE

[1]S. Yıldız, “Statistical relative uniform convergence of a double sequence of functions at a point and applications to approximation theory”, CSJ, vol. 42, no. 1, pp. 123–131, Mar. 2021, doi: 10.17776/csj.831339.

ISNAD

Yıldız, Sevda. “Statistical Relative Uniform Convergence of a Double Sequence of Functions at a Point and Applications to Approximation Theory”. Cumhuriyet Science Journal 42/1 (March 1, 2021): 123-131. https://doi.org/10.17776/csj.831339.

JAMA

1.Yıldız S. Statistical relative uniform convergence of a double sequence of functions at a point and applications to approximation theory. CSJ. 2021;42:123–131.

MLA

Yıldız, Sevda. “Statistical Relative Uniform Convergence of a Double Sequence of Functions at a Point and Applications to Approximation Theory”. Cumhuriyet Science Journal, vol. 42, no. 1, Mar. 2021, pp. 123-31, doi:10.17776/csj.831339.

Vancouver

1.Sevda Yıldız. Statistical relative uniform convergence of a double sequence of functions at a point and applications to approximation theory. CSJ. 2021 Mar. 1;42(1):123-31. doi:10.17776/csj.831339

Cited By

Approximation via statistical relative uniform convergence of sequences of functions at a point with respect to power series method

Afrika Matematika

https://doi.org/10.1007/s13370-023-01078-0

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