Statistical extension of bounded sequence space

Year 2021, Volume: 70 Issue: 1, 82 - 99, 30.06.2021

Maya Altınok , Mehmet Küçükaslan , Umutcan Kaya

https://doi.org/10.31801/cfsuasmas.736132

Cited By: 6

Abstract

In this paper by using natural density real valued bounded sequence space $l_{\infty}$ is extented and statistical bounded sequence space $l_{\infty}^{st}$ is obtained. Besides the main properties of the space $l_{\infty}^{st}$, it is shown that $l_{\infty}^{st}$ is a Banach space with a norm produced with the help of density. Also, it is shown
that there is no matrix extension of the space $l_{\infty}$ that its bounded sequences space covers $l_{\infty}^{st}$. Finally, it is shown that the space $l_{\infty}$ is a non-porous subset of $l_{\infty}^{st}$.

Keywords

Natural density, , statistical convergence, statistical sup norm

Project Number

Bu bir projenin sonuçları değildir.

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