## Abstract and Applied Analysis

### On the Domain of the Triangle $A\left(\lambda \right)$ on the Spaces of Null, Convergent, and Bounded Sequences

#### Abstract

We introduce the spaces of $A\left(\lambda \right)$-null, $A\left(\lambda \right)$-convergent, and $A\left(\lambda \right)$-bounded sequences. We examine some topological properties of the spaces and give some inclusion relations concerning these sequence spaces. Furthermore, we compute $\alpha$-, $\beta$-, and $\gamma$-duals of these spaces. Finally, we characterize some classes of matrix transformations from the spaces of $A\left(\lambda \right)$-bounded and $A\left(\lambda \right)$-convergent sequences to the spaces of bounded, almost convergent, almost null, and convergent sequences and present a Steinhaus type theorem.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 476363, 9 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511912

Digital Object Identifier
doi:10.1155/2013/476363

Mathematical Reviews number (MathSciNet)
MR3064395

Zentralblatt MATH identifier
1303.40003

#### Citation

Braha, Naim L.; Başar, Feyzi. On the Domain of the Triangle $A\left(\lambda \right)$ on the Spaces of Null, Convergent, and Bounded Sequences. Abstr. Appl. Anal. 2013 (2013), Article ID 476363, 9 pages. doi:10.1155/2013/476363. https://projecteuclid.org/euclid.aaa/1393511912

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