scholarly journals Statistical extensions of Tauberian theorems for the weighted mean method of summability in two-normed spaces

2021 ◽  
Author(s):  
Hulya Bakicierler ◽  
Ibrahim Canak
Keyword(s):  
Tauberian Theorems ◽  
Normed Spaces ◽  
Weighted Mean

scholarly journals Necessary and sufficient Tauberian conditions for weighted mean methods of summability in two-normed spaces

2020 ◽  
Vol 24 (1) ◽  
pp. 49-57
Author(s):  
İbrahim Çanak ◽  
Gizem Erikli ◽  
Sefa Anıl Sezer ◽  
Ece Yaraşgil
Keyword(s):  
Tauberian Theorems ◽  
Normed Spaces ◽  
Weighted Mean ◽  
Tauberian Conditions ◽  
Necessary And Sufficient

We first define the concept of weighted mean method of summability and then present necessary and sufficient Tauberian conditions for the weighted mean summability of sequences in two-normed spaces. As corollaries, we establish two-normed analogues of two classical Tauberian theorems.

scholarly journals On Tauberian theorems for statistical weighted mean method of summability

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1541-1548 ◽  
Author(s):  
Ümit Totur ◽  
Ibrahim Çanak
Keyword(s):  
Nonnegative Integer ◽  
Statistical Convergence ◽  
Oscillatory Behavior ◽  
Tauberian Theorems ◽  
Real Sequence ◽  
General Control ◽  
Weighted Mean ◽  
Integer Order ◽  
General Control Modulo

In this paper we establish some new Tauberian theorems for the statistical weighted mean method of summability via the weighted general control modulo of the oscillatory behavior of nonnegative integer order of a real sequence. The main results improve the well-known classical Tauberian theorems which are given for weighted mean method of summability and statistical convergence.

scholarly journals Gap Tauberian theorems

1993 ◽  
Vol 47 (3) ◽  
pp. 385-393 ◽  
Author(s):  
Jeff Connor
Keyword(s):  
Tauberian Theorem ◽  
Strong Summability ◽  
Tauberian Theorems ◽  
Weighted Mean ◽  
Tauberian Condition ◽  
Support Set ◽  
Tauberian Conditions ◽  
Summability Matrix ◽  
Regular Summability ◽  
Bk Spaces

In the first section we establish a connection between gap Tauberian conditions and isomorphic copies of Co for perfect coregular conservative BK spaces and in the second we give a characterisation of gap Tauberian conditions for strong summability with respect to a nonnnegative regular summability matrix. These results are used to show that a gap Tauberian condition for strong weighted mean summability is also a gap Tauberian condition for ordinary weighted mean summability. We also make a remark regarding the support set of a matrix and give a Tauberian theorem for a class of conull spaces.

A note on cosine series with coefficients of generalized bounded variation

2020 ◽  
Vol 70 (3) ◽  
pp. 681-688
Author(s):  
Bhikha Lila Ghodadra ◽  
Vanda Fülöp
Keyword(s):  
Bounded Variation ◽  
Tauberian Theorem ◽  
Tauberian Theorems ◽  
Weighted Mean ◽  
Triangular Matrices ◽  
Cosine Series ◽  
Lower Triangular ◽  
Hausdorff Matrices ◽  
Lower Triangular Matrices

AbstractIn this note, we obtain a Tauberian theorem for a class of regular lower triangular matrices operating on cosine series with coefficients tending to zero. As corollaries we obtain Tauberian theorems for weighted mean, Nörlund, and Hausdorff matrices.

scholarly journals TAUBERIAN THEOREMS FOR THE WEIGHTED MEAN METHOD OF SUMMABILITY OF INTEGRALS

2020 ◽  
pp. 775
Author(s):  
Firat Ozsarac ◽  
Ibrahim Canak
Keyword(s):  
Finite Number ◽  
Weight Function ◽  
Generating Function ◽  
Finite Interval ◽  
Classical Type ◽  
Tauberian Theorems ◽  
Weighted Mean ◽  
Positive Weight ◽  
Tauberian Conditions ◽  
Complex Valued

Let $q$ be a positive weight function on $\mathbf{R}_{+}:=[0, \infty)$ which is integrable in Lebesgue's sense over every finite interval $(0,x)$ for $0<x<\infty$, in symbol: $q \in L^{1}_{loc} (\mathbf{R}_{+})$ such that $Q(x):=\int_{0}^{x} q(t) dt\neq 0$ for each $x>0$, $Q(0)=0$ and $Q(x) \rightarrow \infty $ as $x \to \infty $.Given a real or complex-valued function $f \in L^{1}_{loc} (\mathbf{R}_{+})$, we define $s(x):=\int_{0}^{x}f(t)dt$ and$$\tau^{(0)}_q(x):=s(x), \tau^{(m)}_q(x):=\frac{1}{Q(x)}\int_0^x \tau^{(m-1)}_q(t) q(t)dt\,\,\, (x>0, m=1,2,...),$$provided that $Q(x)>0$. We say that $\int_{0}^{\infty}f(x)dx$ is summable to $L$ by the $m$-th iteration of weighted mean method determined by the function $q(x)$, or for short, $(\overline{N},q,m)$ integrable to a finite number $L$ if$$\lim_{x\to \infty}\tau^{(m)}_q(x)=L.$$In this case, we write $s(x)\rightarrow L(\overline{N},q,m)$. It is known thatif the limit $\lim _{x \to \infty} s(x)=L$ exists, then $\lim _{x \to \infty} \tau^{(m)}_q(x)=L$ also exists. However, the converse of this implicationis not always true. Some suitable conditions together with the existence of the limit $\lim _{x \to \infty} \tau^{(m)}_q(x)$, which is so called Tauberian conditions, may imply convergence of $\lim _{x \to \infty} s(x)$. In this paper, one- and two-sided Tauberian conditions in terms of the generating function and its generalizations for $(\overline{N},q,m)$ summable integrals of real- or complex-valued functions have been obtained. Some classical type Tauberian theorems given for Ces\`{a}ro summability $(C,1)$ and weighted mean method of summability $(\overline{N},q)$ have been extended and generalized.  

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.

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