Strong and A-statistical comparisons for sequences

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Demirci K., Khan M., Orhan C.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.278, no.1, pp.27-33, 2003 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 278 Issue: 1
• Publication Date: 2003
• Doi Number: 10.1016/s0022-247x(02)00456-0
• Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.27-33
• Ankara University Affiliated: No

Abstract

Let T and A be two nonnegative regular summability matrices and W(T, p) boolean AND l(infinity) and c(A) (b) denote the spaces of all bounded strongly T-summable sequences with index p > 0, and bounded summability domain of A, respectively. In this paper we show, among other things, that chi(N) is a multiplier from W (T, p) boolean AND l(infinity) into c(A) (b) if and only if any subset K of positive integers that has T-density zero implies that K has A-density zero. These results are used to characterize the A-statistical comparisons for both bounded as well as arbitrary sequences. Using the concept of A-statistical Tauberian rate, we also show that chi(N) is not a multiplier from W (T, p) boolean AND l(infinity) into c(A) (b) that leads to a Steinhaus type result. (C) 2003 Elsevier Science (USA). All rights reserved.