Tauberian conditions under which statistical convergence follows from statistical summability by weighted means

2004 ◽  
Vol 41 (4) ◽  
pp. 391-403 ◽  
Author(s):  
Ferenc Móricz ◽  
Cihan Orhan
Keyword(s):  
Statistical Convergence ◽  
Tauberian Conditions ◽  
Weighted Means

Some Tauberian conditions obtained through weighted generator sequences

2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Cemal Belen
Keyword(s):  
Statistical Convergence ◽  
Weighted Mean ◽  
Tauberian Conditions ◽  
Weighted Means ◽  
Necessary And Sufficient

AbstractRecently, the concept of weighted generator sequence has been introduced by Çanak and Totur [Comput. Math. Appl. 62 (2011), no. 6, 2609–2615]. They proved that certain conditions in terms of weighted generator sequences are Tauberian conditions for the weighted mean method. In this paper, we present the necessary and sufficient Tauberian conditions based on a weighted generator sequence under which statistical convergence follows from statistical summability by weighted means.

Tauberian conditions under which statistical convergence follows from statistical summability by weighted means

2004 ◽  
Vol 41 (4) ◽  
pp. 391-403 ◽  
Author(s):  
Ferenc Móricz ◽  
Cihan Orhan
Keyword(s):  
Finite Number ◽  
Large Class ◽  
Statistical Convergence ◽  
Sufficient Conditions ◽  
Complex Numbers ◽  
Real Numbers ◽  
Tauberian Conditions ◽  
Summability Methods ◽  
Weighted Means ◽  
Necessary And Sufficient

The first named author has recently proved necessary and sufficient Tauberian conditions under which statistical convergence (introduced by H. Fast in 1951) follows from statistical summability (C, 1). The aim of the present paper is to generalize these results to a large class of summability methods (,p) by weighted means. Let p = (pk : k = 0,1, 2,...) be a sequence of nonnegative numbers such that po > 0 and Let (xk) be a sequence of real or complex numbers and set for n = 0,1, 2,.... We present necessary and sufficient conditions under which the existence of the limit st-lim xk = L follows from that of st-lim tn = L, where L is a finite number. If (xk) is a sequence of real numbers, then these are one-sided Tauberian conditions. If (xk) is a sequence of complex numbers, then these are two-sided Tauberian conditions.

scholarly journals Tauberian theorems for weighted mean statistical summability of double sequences of fuzzy numbers

2021 ◽  
Vol 25 (2) ◽  
pp. 175-187
Author(s):  
Hemen Dutta ◽  
Jyotishmaan Gogoi
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Weighted Mean ◽  
Tauberian Conditions ◽  
Weighted Means ◽  
Sequences Of Fuzzy Numbers

We discuss Tauberian conditions under which the statistical convergence of double sequences of fuzzy numbers follows from the statistical convergence of their weighted means. We also prove some other results which are necessary to establish the main results.

scholarly journals Tauberian conditions with controlled oscillatory behavior for statistical convergence

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3853-3865
Author(s):  
Sefa Sezer ◽  
Rahmet Savaş ◽  
İbrahim Çanak
Keyword(s):  
Finite Number ◽  
Statistical Convergence ◽  
Oscillatory Behavior ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Real Sequence ◽  
Tauberian Conditions

We present new Tauberian conditions in terms of the general logarithmic control modulo of the oscillatory behavior of a real sequence (sn) to obtain lim n?? sn = ? from st - lim n?? sn = ?, where ? is a finite number. We also introduce the statistical (l,m) summability method and extend some Tauberian theorems to this method. The main results improve some well-known Tauberian theorems obtained for the statistical convergence.

scholarly journals Some Tauberian conditions on logarithmic density

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Adem Kılıçman ◽  
Stuti Borgohain ◽  
Mehmet Küçükaslan
Keyword(s):  
Statistical Convergence ◽  
Tauberian Theorems ◽  
Logarithmic Density ◽  
Tauberian Conditions ◽  
De La Vallée Poussin

Abstract This article is based on the study on the λ-statistical convergence with respect to the logarithmic density and de la Vallee Poussin mean and generalizes some results of logarithmic λ-statistical convergence and logarithmic $(V,\lambda )$ ( V , λ ) -summability theorems. Hardy’s and Landau’s Tauberian theorems to the statistical convergence, which was introduced by Fast long back in 1951, have been extended by J.A. Fridy and M.K. Khan (Proc. Am. Math. Soc. 128:2347–2355, 2000) in recent years. In this article we try to generalize some Tauberian conditions on logarithmic statistical convergence and logarithmic $(V,\lambda )$ ( V , λ ) -statistical convergence, and we find some new results on it.

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