scholarly journals UNIFORM CONVERGENCE OF MONOTONE SEQUENCES OF FUNCTIONS

1961 ◽  
Vol 47 (4) ◽  
pp. 582-585 ◽  
Author(s):  
S. Bochner
Keyword(s):  
Uniform Convergence ◽  
Monotone Sequences

scholarly journals Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Xuemei Xue ◽  
Jian Tao
Keyword(s):  
Uniform Convergence ◽  
Statistical Convergence ◽  
Banach Lattices ◽  
Order Convergence ◽  
Riesz Spaces ◽  
Monotone Sequences ◽  
Cauchy Sequences ◽  
Relatively Uniform Convergence

A new concept of statistically e-uniform Cauchy sequences is introduced to study statistical order convergence, statistically relatively uniform convergence, and norm statistical convergence in Riesz spaces. We prove that, for statistically e-uniform Cauchy sequences, these three kinds of convergence for sequences coincide. Moreover, we show that the statistical order convergence and the statistically relatively uniform convergence need not be equivalent. Finally, we prove that, for monotone sequences in Banach lattices, the norm statistical convergence coincides with the weak statistical convergence.

scholarly journals Uniform Convergence of Cosine Series With Coefficient from New Class of General Monotone

2019 ◽  
Vol 1 (2) ◽  
pp. 38-42
Author(s):  
Moch Aruman Imron
Keyword(s):  
Uniform Convergence ◽  
Sine Series ◽  
Negative Sequence ◽  
Cosine Series ◽  
New Class ◽  
Series Coefficient ◽  
Monotone Sequences ◽  
The Difference

General monotone sequences class (GMS) has been introduced by Tikhonov. Then Bogdan Szal extended this class to the new class called new class of general monotone. By using non-negative sequence is called 𝛽 to controle the difference of sine series coefficient. By substituting 𝛽 of modulus of sine series coefficient, we study uniform convergence of new class of general monotone on cosine series.

A new application of quasi monotone sequences and quasi power increasing sequences to factored infinite series

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5105-5109
Author(s):  
Hüseyin Bor
Keyword(s):  
Infinite Series ◽  
Summability Factors ◽  
Monotone Sequences ◽  
Power Increasing Sequences ◽  
Weaker Conditions ◽  
Increasing Sequences

In this paper, we generalize a known theorem under more weaker conditions dealing with the generalized absolute Ces?ro summability factors of infinite series by using quasi monotone sequences and quasi power increasing sequences. This theorem also includes some new results.

QUASI-UNIFORM CONVERGENCE AND ℒ-SPACES

1992 ◽  
Vol 18 (2) ◽  
pp. 321 ◽  
Author(s):  
Bukovská ◽  
Bukovský ◽  
Ewert
Keyword(s):  
Uniform Convergence

Topologies Between Compact and Uniform Convergence on Function Spaces, II

1992 ◽  
Vol 18 (1) ◽  
pp. 176 ◽  
Author(s):  
Kundu ◽  
McCoy ◽  
Raha
Keyword(s):  
Uniform Convergence ◽  
Function Spaces

scholarly journals ON THE UNIFORM CONVERGENCE OF DECONVOLUTION ESTIMATORS FROM REPEATED MEASUREMENTS

2021 ◽  
pp. 1-22
Author(s):  
Daisuke Kurisu ◽  
Taisuke Otsu
Keyword(s):  
Multivariate Analysis ◽  
Measurement Error ◽  
Uniform Convergence ◽  
Measurement Errors ◽  
Convergence Rates ◽  
Free Variable ◽  
Error Model ◽  
Repeated Measurements ◽  
Empirical Characteristic Function ◽  
Measurement Error Model

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491–533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions.

scholarly journals Limit of 𝑝-Laplacian obstacle problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raffaela Capitanelli ◽  
Maria Agostina Vivaldi
Keyword(s):  
Asymptotic Behavior ◽  
Uniform Convergence ◽  
Explicit Expression ◽  
Positive Measure ◽  
Sufficient Conditions ◽  
Obstacle Problems ◽  
Dimensional Case ◽  
Asymptotic Behavior Of Solutions ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as {p\to\infty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in Ω or for data f (that do not change sign in Ω) possibly vanishing in a set of positive measure.

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