## Journal of Mathematics of Kyoto University

### Lacunary $A_{p}$-summable sequence spaces defined by Orlicz functions

Tunay Bilgin

#### Abstract

In this paper we introduce some new sequence spaces combining a lacunary sequence, an infinite matrix, a bounded sequence and an Orlicz function. We discuss some topological properties and establish some inclusion relations between these spaces. It is also shown that if a sequence is lacunary $A_{p}$-convergent with respect to an Orlicz function then it is lacunary strongly $S^{\theta}(A)$-statistically convergent.

#### Article information

Source
J. Math. Kyoto Univ., Volume 46, Number 2 (2006), 367-376.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250281782

Digital Object Identifier
doi:10.1215/kjm/1250281782

Mathematical Reviews number (MathSciNet)
MR2284349

Zentralblatt MATH identifier
1128.40002

#### Citation

Bilgin, Tunay. Lacunary $A_{p}$-summable sequence spaces defined by Orlicz functions. J. Math. Kyoto Univ. 46 (2006), no. 2, 367--376. doi:10.1215/kjm/1250281782. https://projecteuclid.org/euclid.kjm/1250281782