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2020 Generalized almost statistical convergence
Biswa Ranjan Datta, Absos Ali Shaikh
Real Anal. Exchange 45(2): 439-452 (2020). DOI: 10.14321/realanalexch.45.2.0439

Abstract

The objective of this paper is to introduce the notion of generalized almost statistical (briefly, GAS) convergence of bounded real sequences, which generalizes the notion of almost convergence as well as statistical convergence of bounded real sequences. As a special kind of Banach limit functional, we also introduce the concept of Banach statistical limit functional and the notion of GAS convergence mainly depends on the existence of Banach statistical limit functional. We prove the existence of Banach statistical limit functional. Then we have shown the existence of a GAS convergent sequence, which is neither statistical convergent nor almost convergent. Also, some topological properties of the space of all GAS convergent sequences are investigated.

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Biswa Ranjan Datta. Absos Ali Shaikh. "Generalized almost statistical convergence." Real Anal. Exchange 45 (2) 439 - 452, 2020. https://doi.org/10.14321/realanalexch.45.2.0439

Information

Published: 2020
First available in Project Euclid: 30 June 2020

zbMATH: 07229057
Digital Object Identifier: 10.14321/realanalexch.45.2.0439

Subjects:
Primary: 46B45
Secondary: 40A35 , ‎40G15‎ , 40H05

Keywords: ‎almost convergence‎ , Banach limit functional , statistical convergence

Rights: Copyright © 2020 Michigan State University Press

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Vol.45 • No. 2 • 2020
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