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

S. A. Mohiuddine, Bipan Hazarika, Abdullah Alotaibi
2013 Abstract and Applied Analysis  
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 doubleθ-summable and double statistically lacunary summable in locally solid Riesz space and establish a relationship between these notions.
doi:10.1155/2013/507962 fatcat:ejlt6a2ynnh5ta4nijp5vyzyo4