Strong Convergence Theorems for Nonexpansive Semigroups without Bochner Integrals

Strong Convergence Theorems for Nonexpansive Semigroups without Bochner Integrals

Strong Convergence Theorems of the CQ Method for Nonexpansive Semigroups

Throughout this paper, letH be a real Hilbert space with inner product 〈·,·〉 and ‖ · ‖. We use xn⇀ x to indicate that the sequence {xn} converges weakly to x. Similarly, xn → x will symbolize strong convergence. we denote by N and R+ the sets of nonnegative integers and nonnegative real numbers, respectively. let C be a closed convex subset of a Hilbert space H , and Let T : C → C be a nonexpan...

Strong Convergence Theorems for Asymptotically Nonexpansive Mappings and Asymptotically Nonexpansive Semigroups

A point x ∈ C is a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T ; that is, F(T)= {x ∈ C : Tx = x}. Also, recall that a family S= {T(s) | 0≤ s <∞} of mappings from C into itself is called an asymptotically nonexpansive semigroup on C if it satisfies the following conditions: (i) T(0)x = x for all x ∈ C; (ii) T(s+ t)= T(s)T(t) for all s, t ≥ 0; (iii) there exists ...

ON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...

Strong Convergence Theorems for Nonexpansive Semigroups and Variational Inequalities in Banach Spaces

Let X be a uniformly convex Banach space and S {T s : 0 ≤ s < ∞} be a nonexpansive semigroup such that F S ⋂s>0 F T s / ∅. Consider the iterative method that generates the sequence {xn} by the algorithm xn 1 αnf xn βnxn 1 − αn − βn 1/sn ∫sn 0 T s xnds, n ≥ 0, where {αn}, {βn}, and {sn} are three sequences satisfying certain conditions, f : C → C is a contraction mapping. Strong convergence of t...