STRONG CONVERGENCE OF COMPOSITE ITERATIVE METHODS FOR NONEXPANSIVE MAPPINGS

- Journal title : Journal of the Korean Mathematical Society
- Volume 46, Issue 6, 2009, pp.1151-1164
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2009.46.6.1151

Title & Authors

STRONG CONVERGENCE OF COMPOSITE ITERATIVE METHODS FOR NONEXPANSIVE MAPPINGS

Jung, Jong-Soo;

Jung, Jong-Soo;

Abstract

Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C C a contractive mapping (or a weakly contractive mapping), and T : C C a nonexpansive mapping with the fixed point set F(T) . Let {} be generated by a new composite iterative scheme: , , (). It is proved that {} converges strongly to a point in F(T), which is a solution of certain variational inequality provided the sequence {} (0, 1) satisfies = 0 and , {} [0, a) for some 0 < a < 1 and the sequence {} is asymptotically regular.

Keywords

viscosity approximation method;nonexpansive mapping;composite iterative scheme;contractive mapping;weakly contractive mapping;weakly sequentially continuous duality mapping;variational inequality;

Language

English

Cited by

1.

2.

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