Strong Convergence

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Philip E. Cheng - One of the best experts on this subject based on the ideXlab platform.

  • A note on Strong Convergence rates in nonparametric regression
    Statistics & Probability Letters, 1995
    Co-Authors: Philip E. Cheng
    Abstract:

    The Strong Convergence rates in nonparametric regression estimation have been mostly discussed when the error variables in the regression models have finite variances. A few recent studies concern heavy-tailed error distributions for two comparable methods using the kernel and the k-nearest neighbor estimators. The obtained Convergence rates are however noncomparable. Assuming the error variables have finite pth moments for the same p, 1 < p < 2, we derive comparable Strong Convergence rates for these two estimators via a unified approach. This improves the existing results for both the kernel estimator and the k-nearest neighbor estimator.

Hafiz Fukhar-ud-din - One of the best experts on this subject based on the ideXlab platform.

  • Strong Convergence of an Ishikawa-type algorithm in CAT(0) spaces
    Fixed Point Theory and Applications, 2013
    Co-Authors: Hafiz Fukhar-ud-din
    Abstract:

    We study Strong Convergence of an Ishikawa-type algorithm of two asymptotically nonexpansive type maps to their common fixed point on a space. Our work provides an affirmative answer to the question of Tan and Xu (Proc. Am. Math. Soc. 122:733-739, 1994); in particular, Strong Convergence of an Ishikawa-type algorithm of two asymptotically nonexpansive maps without the rate of Convergence condition is obtained on a nonlinear domain. MSC:47H09, 47H10, 49M05.

  • Strong Convergence by the shrinking effect of two half-spaces and applications
    Fixed Point Theory and Applications, 2013
    Co-Authors: Muhammad Aqeel Ahmad Khan, Hafiz Fukhar-ud-din
    Abstract:

    This paper provides a new hybrid-type shrinking projection method for Strong Convergence results in a Hilbert space. The paper continues - by utilizing the proposed hybrid algorithm - with a Strong Convergence towards an approximate common element of the set of solutions of a finite family of generalized equilibrium problems and the set of common fixed points of two finite families of k-strict pseudo-contractions in a Hilbert space. Comparatively, our results improve and extend various results announced in the current literature.

Naza Tanović-miller - One of the best experts on this subject based on the ideXlab platform.

  • Strong boundedness and Strong Convergence in sequence spaces
    Canadian Journal of Mathematics, 1991
    Co-Authors: Martin Buntinas, Naza Tanović-miller
    Abstract:

    AbstractStrong Convergence has been investigated in summability theory and Fourier analysis. This paper extends Strong Convergence to a topological property of sequence spaces E. The more general property of Strong boundedness is also defined and examined. One of the main results shows that for an FK-space E which contains all finite sequences, Strong Convergence is equivalent to the invariance property E = ℓ ν0. E with respect to coordinatewise multiplication by sequences in the space ℓν0 defined in the paper. Similarly, Strong boundedness is equivalent to another invariance E = ℓν.E. The results of the paper are applied to summability fields and spaces of Fourier series.

Wataru Takahashi - One of the best experts on this subject based on the ideXlab platform.

Gilles Pisier - One of the best experts on this subject based on the ideXlab platform.

  • Strong Convergence for reduced free products
    Infinite Dimensional Analysis Quantum Probability and Related Topics, 2016
    Co-Authors: Gilles Pisier
    Abstract:

    Using an inequality due to Ricard and Xu, we give a different proof of Paul Skoufranis’s recent result showing that the Strong Convergence of possibly non-commutative random variables X(k) → X is stable under reduced free product with a fixed non-commutative random variable Y. In fact we obtain a more general fact: assuming that the families X(k) = {X i(k)} and Y(k) = {Y j(k)} are ∗-free as well as their limits (in moments) X = {Xi} and Y = {Yj}, the Strong Convergences X(k) → X and Y(k) → Y imply that of {X(k),Y(k)} to {X,Y }. Phrased in more striking language: the reduced free product is “continuous” with respect to Strong Convergence. The analogue for weak Convergence (i.e. Convergence of all moments) is obvious. Our approach extends to the amalgamated free product, left open by Skoufranis.

  • Strong Convergence for reduced free products
    Infinite Dimensional Analysis Quantum Probability and Related Topics, 2016
    Co-Authors: Gilles Pisier
    Abstract:

    Using an inequality due to Ricard and Xu, we give a different proof of Paul Skoufranis’s recent result showing that the Strong Convergence of possibly non-commutative random variables [Formula: see text] is stable under reduced free product with a fixed non-commutative random variable [Formula: see text]. In fact we obtain a more general fact: assuming that the families [Formula: see text] and [Formula: see text] are ∗-free as well as their limits (in moments) [Formula: see text] and [Formula: see text], the Strong Convergences [Formula: see text] and [Formula: see text] imply that of [Formula: see text] to [Formula: see text]. Phrased in more striking language: the reduced free product is “continuous” with respect to Strong Convergence. The analogue for weak Convergence (i.e. Convergence of all moments) is obvious. Our approach extends to the amalgamated free product, left open by Skoufranis.