Journal of Mathematics of Kyoto University

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

Tunay Bilgin

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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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250281782

Digital Object Identifier
doi:10.1215/kjm/1250281782

Mathematical Reviews number (MathSciNet)
MR2284349

Zentralblatt MATH identifier
1128.40002

Subjects
Primary: 46B45: Banach sequence spaces [See also 46A45]
Secondary: 40A05: Convergence and divergence of series and sequences 46A45: Sequence spaces (including Köthe sequence spaces) [See also 46B45]

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


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