Some Tauberian Theorems for the Weighted Mean Method of Summability of Double Sequences
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let p = (pj) and q = (qk) be real sequences of nonnegative numbers with the property thatPm= n-ary sumation j=0mpj not equal 0andQm= n-ary sumation k=0nqk not equal 0forallmandn.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{ccccccc}{P}_{m}=\sum_{j=0}<^>{m}{p}_{j}\ne 0& {\text{and}}& {Q}_{m}=\sum_{k=0}<^>{n}{q}_{k}\ne 0& \mathrm{for all}& m& {\text{and}}& n.\end{array}$$\end{document}Also let (Pm) and (Qn) be regularly varying positive indices. Assume that (umn) is a double sequence of complex (real) numbers, which is (N over bar \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{N }$$\end{document}, p, q; alpha, beta)-summable and has a finite limit, where (alpha, beta) = (1, 1), (1, 0), or (0, 1). We present some conditions imposed on the weights under which (umn) converges in Pringsheim's sense. These results generalize and extend the results obtained by the authors in [Comput. Math. Appl., 62, No. 6, 2609-2615 (2011)].
Açıklama
Anahtar Kelimeler
Power-Series Methods, Statistical Convergence
Kaynak
Ukrainian Mathematical Journal
WoS Q Değeri
N/A
Scopus Q Değeri
Q3
