A GENERAL VISCOSITY APPROXIMATION METHOD OF FIXED POINT SOLUTIONS OF VARIATIONAL INEQUALITIES FOR NONEXPANSIVE SEMIGROUPS IN HILBERT SPACES

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 45, Issue 4, 2008, pp.717-728
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2008.45.4.717

Title & Authors

A GENERAL VISCOSITY APPROXIMATION METHOD OF FIXED POINT SOLUTIONS OF VARIATIONAL INEQUALITIES FOR NONEXPANSIVE SEMIGROUPS IN HILBERT SPACES

Plubtieng, Somyot; Wangkeeree, Rattanaporn;

Plubtieng, Somyot; Wangkeeree, Rattanaporn;

Abstract

Let H be a real Hilbert space and S = {T(s) : <} be a nonexpansive semigroup on H such that For a contraction f with coefficient 0 < < 1, a strongly positive bounded linear operator A with coefficient > 0. Let 0 < < . It is proved that the sequences {} and {} generated by the iterative method and where {t}, {} (0, 1) and {}, {} are positive real divergent sequences, converges strongly to a common fixed point which solves the variational inequality for .

Keywords

fixed point;variational inequality;viscosity approximation;nonexpansive semigroup;strong convergence;

Language

English

Cited by

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