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Abstract and Applied Analysis
Volume 2014, Article ID 858504, 8 pages
http://dx.doi.org/10.1155/2014/858504
Research Article

Some New Lacunary Strong Convergent Vector-Valued Sequence Spaces

1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3Department of Mathematics, Model Institute of Engineering & Technology, Kot Bhalwal 181122, India

Received 29 March 2014; Accepted 28 June 2014; Published 24 July 2014

Academic Editor: Hassan Eltayeb

Copyright © 2014 M. Mursaleen 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 introduce some vector-valued sequence spaces defined by a Musielak-Orlicz function and the concepts of lacunary convergence and strong ( )-convergence, where is an infinite matrix of complex numbers. We also make an effort to study some topological properties and some inclusion relations between these spaces.