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AN IMPLICIT ITERATION PROCESS FOR NONEXPANSIVE MAPPINGS

We prove the convergence of an implicit iteration process to a common fixed point of a finite family of nonexpansive mappings in a Hilbert space.

286 73

VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE MAPPINGS

- H. Xu
- Mathematics
- 1 October 2004

Abstract Viscosity approximation methods for nonexpansive mappings are studied. Consider a nonexpansive self-mapping T of a closed convex subset C of a Banach space X. Suppose that the set Fix( T )… Expand

871 53

A general iterative method for nonexpansive mappings in Hilbert spaces

Let H be a real Hilbert space. Consider on H a nonexpansive mapping T with a fixed point, a contraction f with coefficient 0 0. Let 0

513 43

Iterative Algorithms for Nonlinear Operators

- H. Xu
- Mathematics
- 1 August 2002

Iterative algorithms for nonexpansive mappings and maximal monotone operators are investigated. Strong convergence theorems are proved for nonexpansive mappings, including an improvement of a result… Expand

1,362 42

Inequalities in Banach spaces with applications

- H. Xu
- Mathematics
- 1 June 1991

well known that many problems in a Hilbert space H are solved by applying the following identity: IlAx + (1 - A)YI12 = a412 + (1 - ~)llYl12 - A(1 - Mx - Yl12 (1.1) for all x, y in H and 0 5 I 5 1.… Expand

1,045 39

Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities

AbstractAssume that F is a nonlinear operator on a real Hilbert space H which is η-strongly monotone and κ-Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the… Expand

288 23

WEAK AND STRONG CONVERGENCE THEOREMS FOR STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACES

Abstract Let C be a closed convex subset of a real Hilbert space H and assume that T is a κ -strict pseudo-contraction on C with a fixed point, for some 0 ⩽ κ 1 . Given an initial guess x 0 ∈ C and… Expand

468 18- PDF

Strong convergence of modified Mann iterations

Abstract The Mann iterations for nonexpansive mappings have only weak convergence even in a Hilbert space. We propose two modifications of the Mann iterations in a uniformly smooth Banach space, one… Expand

236 17

Iterative methods for strict pseudo-contractions in Hilbert spaces

- G. L. Acedo, H. Xu
- Mathematics
- 1 October 2007

Abstract Let { T i } i = 1 N be N strict pseudo-contractions defined on a closed convex subset C of a real Hilbert space H . Consider the problem of finding a common fixed point of these mappings and… Expand

187 16

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