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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.
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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
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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
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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 resultExpand
  • 1,362
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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
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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 theExpand
  • 288
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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 andExpand
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  • 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, oneExpand
  • 236
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Iterative methods for strict pseudo-contractions in Hilbert spaces
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 andExpand
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