2,235 research outputs found
Viscosity approximation methods for nonexpansive mappings and monotone mappings
AbstractViscosity approximation methods for nonexpansive mappings are studied. Consider the iteration process {xn}, where x0∈C is arbitrary and xn+1=αnf(xn)+(1−αn)SPC(xn−λnAxn), f is a contraction on C, S is a nonexpansive self-mapping of a closed convex subset C of a Hilbert space H. It is shown that {xn} converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality
On Strong convergence of Halpern's method using averaged type mappings
In this paper, inspired by Iemoto and Takahashi [S. Iemoto, W. Takahashi,
Nonlinear Analysis 71, (2009), 2082-2089], we study the Halpern's method to
approximate strongly fixed points of a nonexpansive mapping and of a
nonspreading mapping. A crucial tool in our results is the regularization with
the averaged type mappings [C. Byrne, Inverse Probl. 20, (2004), 103-120]
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