International Journal of Advanced and Applied Sciences
Int. j. adv. appl. sci.
EISSN: 2313-3724
Print ISSN: 2313-626X
Volume 4, Issue 1 (January 2017), Pages: 96-101
Title: Slowly oscillating sequences in locally normal Riesz spaces
Author(s): Bipan Hazarika 1, *, M. Kemal Ozdemir 2, Ayhan Esi 3
Affiliation(s):
1Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh-791112, Arunachal Pradesh, India
2Department of Mathematics, Science and Arts Faculty, Inonu University, Malatya, Turkey
3Department of Mathematics, Science and Arts Faculty, Adiyaman University, Adiyaman, Turkey
https://doi.org/10.21833/ijaas.2017.01.014
Abstract:
In the present paper, we are going to introduce and at the same time investigate the notion of slowly oscillating sequences, study on slowly oscillating compactness and slowly oscillating continuous functions in locally normal Riesz space. For this purpose, first of all, we are going to try to put forward some fundamental theorems about oscillating continuity, slowly oscillating compactness, sequential continuity and uniform continuity. Secondly, the newly obtained results in this paper can also be obtained with the definition of quasi-slowly oscillating and Δ-quasi-slowly oscillating sequences in terms of fuzzy points. Finally, most of the related theorems and lemmas are presented clearly.
© 2017 The Authors. Published by IASE.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Riesz space Continuity, Quasi-Cauchy sequence, Slowly oscillating sequences
Article History: Received 2 November 2016, Received in revised form 23 December 2016, Accepted 9 January 2017
Digital Object Identifier:
https://doi.org/10.21833/ijaas.2017.01.014
Citation:
Hazarika B, Ozdemir MK, and Esi A (2017). Slowly oscillating sequences in locally normal Riesz spaces. International Journal of Advanced and Applied Sciences, 4(1): 96-101
http://www.science-gate.com/IJAAS/V4I1/Hazarika.html
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