scholarly journals Sufficient conditions for uniform convergence of random series

2020 ◽  
Vol 3 (1) ◽  
pp. 32-34
Author(s):  
M. Akbarov ◽  
Sh.O. Sobirov ◽  
S. Kukieva
Keyword(s):  
Uniform Convergence ◽  
Sufficient Conditions ◽  
Random Series

Sufficient conditions for the uniform convergence of random series are obtained.

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.

Completeness of the L1-space of closed vector measures

1990 ◽  
Vol 33 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Werner J. Ricker
Keyword(s):  
Uniform Convergence ◽  
Convex Space ◽  
Vector Measure ◽  
Sufficient Conditions ◽  
Locally Convex Space ◽  
Vector Measures ◽  
Locally Convex

The notion of a closed vector measure m, due to I. Kluv´;nek, is by now well established. Its importance stems from the fact that if the locally convex space X in which m assumes its values is sequentially complete, then m is closed if and only if its L1-space is complete for the topology of uniform convergence of indefinite integrals. However, there are important examples of X-valued measures where X is not sequentially complete. Sufficient conditions guaranteeing the completeness of L1(m) for closed X-valued measures m are presented without the requirement that X be sequentially complete.

scholarly journals Uniform Convergence and Transitive Subsets

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Lei Liu ◽  
Shuli Zhao ◽  
Hongliang Liang
Keyword(s):  
Uniform Convergence ◽  
Metric Space ◽  
Sufficient Conditions ◽  
Continuous Maps

Let(X,d)be a metric space and a sequence of continuous mapsfn:X→Xthat converges uniformly to a mapf. We investigate the transitive subsets offnwhether they can be inherited byfor not. We give sufficient conditions such that the limit mapfhas a transitive subset. In particular, we show the transitive subsets offnthat can be inherited byfiffnconverges uniformly strongly tof.

Sufficient Conditions for Uniform Convergence on Layer-Adapted Grids

Computing ◽  
1999 ◽  
Vol 63 (1) ◽  
pp. 27-45 ◽  
Author(s):  
H.-G. Roos ◽  
T. Linß Not Available
Keyword(s):  
Uniform Convergence ◽  
Sufficient Conditions

scholarly journals On the convergence of Cesàro means of negative order of Vilenkin-Fourier series

2019 ◽  
Vol 56 (1) ◽  
pp. 22-44
Author(s):  
Gvantsa Shavardenidze
Keyword(s):  
Fourier Series ◽  
Continuous Function ◽  
Uniform Convergence ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Cesàro Means ◽  
Cesaro Means ◽  
Negative Order ◽  
Cesáro Means

Abstract In 1971 Onnewer and Waterman establish a sufficient condition which guarantees uniform convergence of Vilenkin-Fourier series of continuous function. In this paper we consider different classes of functions of generalized bounded oscillation and in the terms of these classes there are established sufficient conditions for uniform convergence of Cesàro means of negative order.

scholarly journals On convergence of branched continued fraction expansions of Horn's hypergeometric function $H_3$ ratios

2021 ◽  
Vol 13 (3) ◽  
pp. 642-650
Author(s):  
T.M. Antonova
Keyword(s):  
Uniform Convergence ◽  
Hypergeometric Function ◽  
Compact Subset ◽  
Complex Variable ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Continued Fraction Expansions ◽  
Branched Continued Fraction

The paper deals with the problem of convergence of the branched continued fractions with two branches of branching which are used to approximate the ratios of Horn's hypergeometric function $H_3(a,b;c;{\bf z})$. The case of real parameters $c\geq a\geq 0,$ $c\geq b\geq 0,$ $c\neq 0,$ and complex variable ${\bf z}=(z_1,z_2)$ is considered. First, it is proved the convergence of the branched continued fraction for ${\bf z}\in G_{\bf h}$, where $G_{\bf h}$ is two-dimensional disk. Using this result, sufficient conditions for the uniform convergence of the above mentioned branched continued fraction on every compact subset of the domain $\displaystyle H=\bigcup_{\varphi\in(-\pi/2,\pi/2)}G_\varphi,$ where \[\begin{split} G_{\varphi}=\big\{{\bf z}\in\mathbb{C}^{2}:&\;{\rm Re}(z_1e^{-i\varphi})<\lambda_1 \cos\varphi,\; |{\rm Re}(z_2e^{-i\varphi})|<\lambda_2 \cos\varphi, \\ &\;|z_k|+{\rm Re}(z_ke^{-2i\varphi})<\nu_k\cos^2\varphi,\;k=1,2;\; \\ &\; |z_1z_2|-{\rm Re}(z_1z_2e^{-2\varphi})<\nu_3\cos^{2}\varphi\big\}, \end{split}\] are established.

scholarly journals Approximation by double Walsh polynomials

1992 ◽  
Vol 15 (2) ◽  
pp. 209-220 ◽  
Author(s):  
Ferenc Móricz
Keyword(s):  
Banach Space ◽  
Fourier Series ◽  
Uniform Convergence ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Partial Sums ◽  
Lipschitz Classes ◽  
Sufficient Conditions For Convergence ◽  
By Products ◽  
De La Vallée Poussin

We study the rate of approximation by rectangular partial sums, Cesàro means, and de la Vallée Poussin means of double Walsh-Fourier series of a function in a homogeneous Banach spaceX. In particular,Xmay beLp(I2), where1≦p<∞andI2=[0,1)×[0,1), orCW(I2), the latter being the collection of uniformlyW-continuous functions onI2. We extend the results by Watari, Fine, Yano, Jastrebova, Bljumin, Esfahanizadeh and Siddiqi from univariate to multivariate cases. As by-products, we deduce sufficient conditions for convergence inLp(I2)-norm and uniform convergence onI2as well as characterizations of Lipschitz classes of functions. At the end, we raise three problems.

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