On New Difference Sequence Space and Their Generalised Almost Statistical Convergence

Authors(1) :-Ajaya Kumar Singh

The object of the present paper is to introduce the notion of generalised almost statistical (GAS) convergence of bounded real sequences, which generalises the notion of almost convergence as well as statistical convergence of bounded real sequences. 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. Also, the existence GAS convergent sequence, which is neither statistical convergent nor almost convergent. Lastly, some topological properties of the space of all GAS convergent sequences are investigated.

Authors and Affiliations

Ajaya Kumar Singh
Department of Mathematics, Ekamra College, Bhubaneswar, Odisha, India.

Banach limits, Banach statistical limit functional, Linear functional, Almost convergence, Generalised almost convergence, Generalised almost statistical convergence.

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Publication Details

Published in : Volume 7 | Issue 1 | January-February 2020
Date of Publication : 2020-02-29
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 212-219
Manuscript Number : IJSRST207144
Publisher : Technoscience Academy

Print ISSN : 2395-6011, Online ISSN : 2395-602X

Cite This Article :

Ajaya Kumar Singh, " On New Difference Sequence Space and Their Generalised Almost Statistical Convergence", International Journal of Scientific Research in Science and Technology(IJSRST), Print ISSN : 2395-6011, Online ISSN : 2395-602X, Volume 7, Issue 1, pp.212-219, January-February-2020. Available at doi : https://doi.org/10.32628/IJSRST207144    
Journal URL : https://ijsrst.com/IJSRST207144
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