Tauberian Conditions Under Which Convergence Follows from Statistical Summability by Weighted Means

2018 ◽  
pp. 1-22
Author(s):  
Zerrin Önder ◽  
İbrahim Çanak
Keyword(s):  
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 Necessary and sufficient conditions under which convergence follows from summability by weighted means

2001 ◽  
Vol 27 (7) ◽  
pp. 399-406 ◽  
Author(s):  
Ferenc Móricz ◽  
Ulrich Stadtmüller
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Complex Numbers ◽  
Real Numbers ◽  
Weighted Mean ◽  
Tauberian Conditions ◽  
Weighted Means ◽  
Necessary And Sufficient

We prove necessary and sufficient Tauberian conditions for sequences summable by weighted mean methods. The main results of this paper apply to all weighted mean methods and unify the results known in the literature for particular methods. Among others, the conditions in our theorems are easy consequences of the slowly decreasing condition for real numbers, or slowly oscillating condition for complex numbers. Therefore, practically all classical (one-sided as well as two-sided) Tauberian conditions for weighted mean methods are corollaries of our two main theorems.

scholarly journals Spatio-temporal expectile regression models

2019 ◽  
Vol 20 (4) ◽  
pp. 386-409
Author(s):  
Elmar Spiegel ◽  
Thomas Kneib ◽  
Fabian Otto-Sobotka
Keyword(s):  
Tensor Product ◽  
Least Squares Regression ◽  
Expectile Regression ◽  
Specific Distribution ◽  
Weighted Means ◽  
Temporal Models ◽  
Error Terms ◽  
Spatio Temporal ◽  
Set Up ◽  
Main Effects

Spatio-temporal models are becoming increasingly popular in recent regression research. However, they usually rely on the assumption of a specific parametric distribution for the response and/or homoscedastic error terms. In this article, we propose to apply semiparametric expectile regression to model spatio-temporal effects beyond the mean. Besides the removal of the assumption of a specific distribution and homoscedasticity, with expectile regression the whole distribution of the response can be estimated. For the use of expectiles, we interpret them as weighted means and estimate them by established tools of (penalized) least squares regression. The spatio-temporal effect is set up as an interaction between time and space either based on trivariate tensor product P-splines or the tensor product of a Gaussian Markov random field and a univariate P-spline. Importantly, the model can easily be split up into main effects and interactions to facilitate interpretation. The method is presented along the analysis of spatio-temporal variation of temperatures in Germany from 1980 to 2014.

scholarly journals Weighted Means, Strict Ergodicity, and Uniform Distributions

2005 ◽  
Vol 78 (3-4) ◽  
pp. 329-337 ◽  
Author(s):  
V. V. Kozlov
Keyword(s):  
Uniform Distributions ◽  
Weighted Means
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