×

Properties of some \(q\)-Hausdorff matrices. (English) Zbl 1291.15091

Summary: We show that the \(C_q\) matrices, the \(q\)-Hausdorff analogs of the Cesàro matrix of order 1, are all equivalent to convergence, and that the same is true of the \(q\)-Hölder matrices. We also show that the \(C_q\) matrices of order \({\alpha}\), for each each positive \({\alpha}\), are regular.

MSC:

15B99 Special matrices
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Albayrak, Inci; Rhoades, B. E., The question of equivalence for generalized Hausdorff matrices, J. Math. Anal. Appl., 328, 414-428 (2007) · Zbl 1112.15025
[2] Aydin Akgun, F.; Rhoades, B. E., Factorable generalized Hausdorff matrices, J. Adv. Math. Stud., 3, 1-8 (2010) · Zbl 1204.40005
[3] Bennett, Grahame, An inequality for Hausdorff means, Houston J. Math., 25, 709-743 (1999) · Zbl 0977.26006
[4] Bustoz, Joaquin; Gordillo, Luis F., q-Hausdorff summability, J. Comput. Anal. Appl., 7, 35-48 (2005) · Zbl 1083.40004
[5] Endl, K., Untersuchen über Momentprobleme bei Verfahren vom Hausdorffschen Typus, Math. Ann., 139, 403-432 (1960) · Zbl 0127.02702
[6] Hardy, G. H., Divergent Series (1949), Cambridge University Press · Zbl 0032.05801
[7] Hausdorff, F., Summationmethoden und Momentfolgen, I Math. Z, 9, 74-109 (1921) · JFM 48.2005.01
[8] Hausdorff, F., Summationmethoden und Momentfolgen, II Math. Z, 9, 280-299 (1921) · JFM 48.2005.02
[9] Hurwitz, W. A.; Silverman, L. L., On the consistency and equivalence of certain definitions of summability, Trans. Am. Math. Soc., 18, 1-20 (1917) · JFM 46.0321.03
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.