Necessary and sufficient conditions for inclusion relations for absolute summability

Rhoades, B.E.; SAVAŞ, EKREM

doi:10.1007/bf02829605

Necessary and sufficient conditions for inclusion relations for absolute summability

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Rhoades B., SAVAŞ E.

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, vol.113, no.3, pp.243-250, 2003 (SCI-Expanded)

Publication Type: Article / Article
Volume: 113 Issue: 3
Publication Date: 2003
Doi Number: 10.1007/bf02829605
Journal Name: Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Page Numbers: pp.243-250
Keywords: Absolute summability, Cesáro matrix, Weighted mean matrix
Uşak University Affiliated: Yes

Abstract

We obtain a set of necessary and sufficient conditions for |N̄, pn|k to imply |N̄, qn|s for 1 < k ≤ s < ∞. Using this result we establish several inclusion theorems as well as conditions for the equivalence of |N̄, pn|k and |N̄, qn|s.