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

作者：Mohiuddine S A^*; Hazarika Bipan; Alotaibi Abdullah

来源：Abstract and Applied Analysis, 2013, 2013: 507962.

DOI：10.1155/2013/507962

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 theta-summable and double statistically lacunary summable in locally solid Riesz space and establish a relationship between these notions.

• 出版日期2013