International Journal of Advanced and Applied Sciences
Int. j. adv. appl. sci.
EISSN: 2313-3724
Print ISSN: 2313-626X
Volume 4, Issue 5 (May 2017), Pages: 101-108
Title: The ∫ πͺπππ° statistical convergence of real numbers over Musielak π-metric space
Author(s): M. Kemal Ozdemir 1, *, Subramanian Nagarajan 2, Ayhan Esi 3
Affiliation(s):
1Department of Mathematics, Science and Arts Faculty, Inonu University, 44280, Malatya, Turkey
2Department of Mathematics, SASTRA University, Thanjavur-613 401, India
3Department of Mathematics, Science and Arts Faculty, Adiyaman University, 02040, Adiyaman, Turkey
https://doi.org/10.21833/ijaas.2017.05.018
Abstract:
In this paper, we introduce the concepts of ∫ πͺπππ° statistical convergence and strongly ∫ πͺπππ° of real numbers. It is also shown that ∫ πͺπππ° statistical convergence and strongly ∫ πͺπππ° are equivalent for analytic sequences of real numbers. We introduce certain new double sequence spaces of ∫ πͺπππ° of fuzzy real numbers defined by I - convergence using sequences of Musielak-Orlicz functions and also study some basic topological and algebraic properties of these spaces, investigate the inclusion relations between these spaces.
© 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: Analytic sequence, Musielak - modulus function, P- metric space, Ideal convergent, Fuzzy number, De la Vallee-Poussin mean
Article History: Received 24 November 2016, Received in revised form 27 March 2017, Accepted 27 March 2017
Digital Object Identifier:
https://doi.org/10.21833/ijaas.2017.05.018
Citation:
Ozdemir MK, Nagarajan S, and Esi A (2017). The ∫ πͺπππ° statistical convergence of real numbers over Musielak π-metric space. International Journal of Advanced and Applied Sciences, 4(5): 101-108
http://www.science-gate.com/IJAAS/V4I5/Ozdemir.html
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