In this paper, a nontrivial generalization of a scalar martingale convergence theorem to the vector case is derived. In particular, a theorem is derived concerning the almxat sure convergence to zero of a (vector) martingale normalized by its (ntatrix) process vaziance. This theorem allows a derivation of almost a~n-e convergence results for least squarea identification algorithms applicable to...

3 Local convergence rate: simple case 2 3.1 Theorem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2 Main estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.3 Convergence rate of the sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.4 Proof of the theorem . . . . . . . . . . . . . . ....

The dominated convergence theorem implies that if (fn) is a sequence of functions on a probability space taking values in the interval [0, 1], and (fn) converges pointwise a.e., then ( ∫ fn) converges to the integral of the pointwise limit. Tao [26] has proved a quantitative version of this theorem: given a uniform bound on the rates of metastable convergence in the hypothesis, there is a bound...

‎A new approximation method for the set of common fixed points of‎ ‎nonexpansive mappings and the set of solutions of systems of‎ ‎variational inequalities is introduced and studied‎. ‎Moreover‎, ‎we‎ ‎apply our main result to obtain strong convergence theorem to a‎ ‎common fixed point of a nonexpannsive mapping and solutions of ‎a ‎system of variational inequalities of an inverse strongly mono...

For simplicity, we adopt the following rules: X is a non empty set, S is a σ-field of subsets of X, M is a σ-measure on S, E is an element of S, F , G are sequences of partial functions from X into R, I is a sequence of extended reals, f , g are partial functions from X to R, s1, s2, s3 are sequences of extended reals, p is an extended real number, n, m are natural numbers, x is an element of X...

In [3] M. Gromov introduced the concept of convergence of Riemannian manifolds and he proved the convergence theorem. Since that time the theorem has been developed in detail (see [5], [7], [2]), and we know that it contains some interesting applications. Nevertheless there seems to be an inadequate way of applying the convergence theorem. The purpose of this paper is to present an example whic...

Banach’s fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the natural metric in their domain, making the applicability of Banach’s theorem limited. We explore how generally we can apply Banach’s fixed point theorem to ...

The main purpose of this study is to discuss the uniform boundednessprinciple in fuzzifying topological linear spaces. At first theconcepts of uniformly boundedness principle and fuzzy equicontinuousfamily of linear operators are proposed, then the relations betweenfuzzy equicontinuous and uniformly bounded are studied, and with thehelp of net convergence, the characterization of fuzzyequiconti...

In this paper, based on viscosity technique with perturbation, we introduce a new non-linear viscosity algorithm for finding a element of the set of fixed points of nonexpansivemulti-valued mappings in a Hilbert space. We derive a strong convergence theorem for thisnew algorithm under appropriate assumptions. Moreover, in support of our results, somenumerical examples (u...