Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/507962 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |