[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7858/eamj.2012.045

VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE SEMINGROUPS AND MONOTONE MAPPPINGS

Zhang, Lijuan (College of Mathematics and Computer, Hebei University)

Publication Information

East Asian mathematical journal / v.28, no.5, 2012 , pp. 597-604 More about this Journal

Abstract

Let C be a nonempty closed convex subset of real Hilbert space H and F = $\{S(t):t{\geq}0\}$ a nonexpansive self-mapping semigroup of C, and $f:C{\rightarrow}C$ is a fixed contractive mapping. Consider the process { $x_n$ } : $\{{x_{n+1}={\beta}_nx_n+(1-{\beta}_n)z_n\\z_n={\alpha}_nf(x_n)+(1-{\alpha}_n)S(t_n)P_C(x_n-r_nAx_n)$ . It is shown that { $x_n$ } converges strongly to a common element of the set of fixed points of nonexpansive semigroups and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.

Keywords

nonexpansive semigroup; viscosity approximation; inverse strongly monotone mapping; variational inequality; fixed point;

Citations & Related Records

Reference

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