Journal of Mathematics of Kyoto University

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

Tunay Bilgin

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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

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

First available in Project Euclid: 14 August 2009

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Zentralblatt MATH identifier

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]


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.

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