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 ?
Weak Convergence of Stochastic Processes: With Applications to Statistical Limit Theorems
Weak convergence in the 1990s is found, whereas convergence after 2003 is seen (see Figure 3).
in [18] presented subgradient extragradient method to solve the split feasibility problem, but all these algorithms have only weak convergence in the infinite-dimensional Hilbert spaces.
In [7], when A = [partial derivative][phi] where [phi] is a proper, convex and lower semicontinuous function, we proved an ergodic theorem and a weak convergence theorem for solutions to (1), by assuming (2), (3), (4) and that [t.
Takahashi: Weak convergence of an iterative sequence for accretive operators in Banach spaces, Fixed Point Theory Appl.
Recently Djafari Rouhani and Khatibzadeh [5] formulated essentially Theorem 1 below that shows that the weak convergence result stated by Baillon and Haraux [2] for the case of a subdifferential operator A has a discrete counterpart for a general maximal monotone operator A.
In cases where we are interested just for the mean square or mean square of the final moments, we use the weak convergence criterion, comparing the various orders of the final moments between the exact solution and the final solution.
The proof of (1) relies on the following weak convergence (2) of a family of finite measures.
In the first place, the strong convergence in which the non conditional mean wages or income converge among regions; weak convergence, on the other hand, corresponds to the case where the median conditional {controlling by determining attributes of differentials) converges among regions.
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.