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STRONG CONVERGENCE OF COMPOSITE ITERATIVE METHODS FOR NONEXPANSIVE MAPPINGS
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 Title & Authors
STRONG CONVERGENCE OF COMPOSITE ITERATIVE METHODS FOR NONEXPANSIVE MAPPINGS
Jung, Jong-Soo;
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 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.
Convergence of a General Composite Iterative Method for a Countable Family of Nonexpansive Mappings, ISRN Applied Mathematics, 2012, 2012, 1  crossref(new windwow)
2.
Strong convergence of a new composite iterative method for equilibrium problems and fixed point problems, Applied Mathematics and Computation, 2010, 215, 11, 3891  crossref(new windwow)
3.
Strong convergence of composite iterative methods for equilibrium problems and fixed point problems, Applied Mathematics and Computation, 2009, 213, 2, 498  crossref(new windwow)
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