Strong convergence theorems for coordinatewise negatively associated random vectors in Hilbert space

Strong Convergence Theorems for Infinitely Nonexpansive Mappings in Hilbert Space

Let C be a nonempty closed convex subset of a Hilbert spaceH, T a self-mapping of C. Recall that T is said to be nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. Construction of fixed points of nonexpansive mappings via Mann’s iteration 1 has extensively been investigated in literature see, e.g., 2–5 and reference therein . But the convergence about Mann’s iteration and Ishikawa’s iterati...

Strong Convergence of Weighted Sums for Negatively Orthant Dependent Random Variables

We discuss in this paper the strong convergence for weighted sums of negatively orthant dependent (NOD) random variables by generalized Gaussian techniques. As a corollary, a Cesaro law of large numbers of i.i.d. random variables is extended in NOD setting by generalized Gaussian techniques.

Weak and Strong Convergence Theorems for Equilibrium Problems and Countable Strict Pseudocontractions Mappings in Hilbert Space

Weak and Strong Convergence Theorems for k-Strictly Pseudo-Contractive in Hilbert Space

LetK be a nonempty closed convex subset of a real Hilbert space H , and assume that Ti : K → H, i = 1, 2...N be a finite family of ki-strictly pseudo-contractive mappings for some 0 ≤ ki ≤ 1 such that ⋂N i=1 F (Ti) = {x ∈ K : x = Tix, i = 1, 2...N} = ∅. For the following iterative algorithm in K, for x1, x ′ 1 ∈ K and u ∈ K, { yn = PK [kxn + (1− k)Σi=1λiTixn] xn+1 = βnxn + (1− βn)yn and { y′ n ...

Strong Convergence Theorems by Generalized Cq Method in Hilbert Spaces

Recently, CQ method has been investigated extensively. However, it is mainly applied to modify Mann, Ishikawa and Halpern iterations to get strong convergence. In this paper, we study the properties of CQ method and proposed a framework. Based on that, we obtain a series of strong convergence theorems. Some of them are the extensions of previous results. On the other hand, CQ method, monotone Q...