weak convergence


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weak convergence

[′wēk kən′vər·jəns]
(mathematics)
A sequence of elements x1, x2,… from a topological vector space X converges weakly if the sequence ƒ(x1), ƒ(x2),… converges for every continuous linear functional ƒ on X.
References in periodicals archive ?
Takahashi: Weak convergence of an iterative sequence for accretive operators in Banach spaces, Fixed Point Theory Appl.
Pardo-Fernandez [10] showed that the weak convergence of multidimensional process is weak convergence of linear combination in each component.
Among specific topics are the role of weak convergence in probability theory, ideals in parabolic sub-algebras of simple Lie algebras, the conjugacy of maximal toral sub-algebras of direct limits of loop algebras, quotients in supergeometry, and symmetry and superstring phenomenology.
An important feature of stabilization is that it yields weak convergence results for the scaled functional [[xi].
In the case where p = [infinity] or q = [infinity] they obtained weak convergence of [R.
Continuity of a triangle functions means continuity with respect to the topology of weak convergence in [[DELTA].
Zembayashi: Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal.
Here X denotes the weak convergence with respect to the space X.
In this article, we establish weak convergence rates of the wavelet estimators in the semi-parametric regression model with p-mixing errors, which enrich existing estimation theories and methods for semi-parametric regression models.
Highlighting the role in functional analysis of invariance and, in particular, of non-compact transformation groups, the book uses the same building blocks relative to transformation groups (such as partitions of domain and partitions of range) in proofs of energy inequalities and in weak convergence lemmas.