Tbilisi Mathematical Journal

Extension of lacunary statistical convergence on vector valued double difference sequence space

Anindita Basu

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Abstract

In this paper the concepts of lacunary vector valued double sequences and $\Delta_{11}$-lacunary statistical convergent vector valued double difference sequences have been introduced. Further, the purpose of this work is to extend the known sequence space in the literature for ordinary single sequences to the double sequence space $\Delta_{11}N_{\theta_{r,s}}(E)$ of lacunary strongly convergent vector valued double sequences. Some inclusion relations among them are also established. Lastly, this paper deals with some results which establish the relationship between various lacunary methods.

Article information

Source
Tbilisi Math. J., Volume 7, Issue 1 (2014), 19-30.

Dates
Received: 7 February 2014
Accepted: 22 March 2014
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528768948

Digital Object Identifier
doi:10.2478/tmj-2014-0002

Mathematical Reviews number (MathSciNet)
MR3313041

Zentralblatt MATH identifier
1317.46005

Subjects
Primary: 46A45: Sequence spaces (including Köthe sequence spaces) [See also 46B45]
Secondary: 46B45: Banach sequence spaces [See also 46A45]

Keywords
Lacunary double sequences statistical convergence lacunary refinement

Citation

Basu, Anindita. Extension of lacunary statistical convergence on vector valued double difference sequence space. Tbilisi Math. J. 7 (2014), no. 1, 19--30. doi:10.2478/tmj-2014-0002. https://projecteuclid.org/euclid.tbilisi/1528768948


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