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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 507962, 8 pages
http://dx.doi.org/10.1155/2013/507962
Research Article

Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh 791 112, India

Received 21 February 2013; Accepted 13 June 2013

Academic Editor: Alberto Parmeggiani

Copyright © 2013 S. A. Mohiuddine et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We define the notions of double statistically convergent and double lacunary statistically convergent sequences in locally solid Riesz space and establish some inclusion relations between them. We also prove an extension of a decomposition theorem in this setup. Further, we introduce the concepts of double θ-summable and double statistically lacunary summable in locally solid Riesz space and establish a relationship between these notions.