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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 101782, 11 pages
http://dx.doi.org/10.1155/2014/101782
Research Article

On Lacunary Mean Ideal Convergence in Generalized Random -Normed Spaces

1Department of Mathematics, Faculty of Science and Arts, King Abdulaziz University (KAU), P.O. Box 80200, Khulais 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Ain Shams University, P.O. Box 1156, Abbassia, Cairo 11566, Egypt
3Department of Statistics, Faculty of Science, Sudan University of Science & Technology, Khartoum, Sudan

Received 6 January 2014; Accepted 17 March 2014; Published 24 April 2014

Academic Editor: Jianming Zhan

Copyright © 2014 Awad A. Bakery and Mustafa M. Mohammed. 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

An ideal is a hereditary and additive family of subsets of positive integers . In this paper, we will introduce the concept of generalized random -normed space as an extension of random -normed space. Also, we study the concept of lacunary mean ( )-ideal convergence and -ideal Cauchy for sequences of complex numbers in the generalized random -norm. We introduce -limit points and -cluster points. Furthermore, Cauchy and -Cauchy sequences in this construction are given. Finally, we find relations among these concepts.