Let H be a real Hilbert space. Consider on H a nonexpansive mapping T with a fixed point, a contraction f with coefficient 0 < α <1, and a strongly positive linear bounded operator A with coefficient γ¯ >0. Let 0 < γ <γ¯/α. It is proved that the sequence {xn} generated by the iterative method xn+1 = (I − αnA)T xn + αnγf (xn) converges strongly to a fixed point ˜x ∈ Fix(T ) which solves the variational inequality (γf −A) ˜x,x − ˜x 0 for x ∈ Fix(T ). Keywords: Nonexpansive mapping; Iterative method; Variational inequality; Fixed point; Projection; Viscosity approximation

a general iterative method for nonexpansive mappings in hilbert spaces

MARINO, Giuseppe;
2006

Abstract

Let H be a real Hilbert space. Consider on H a nonexpansive mapping T with a fixed point, a contraction f with coefficient 0 < α <1, and a strongly positive linear bounded operator A with coefficient γ¯ >0. Let 0 < γ <γ¯/α. It is proved that the sequence {xn} generated by the iterative method xn+1 = (I − αnA)T xn + αnγf (xn) converges strongly to a fixed point ˜x ∈ Fix(T ) which solves the variational inequality (γf −A) ˜x,x − ˜x 0 for x ∈ Fix(T ). Keywords: Nonexpansive mapping; Iterative method; Variational inequality; Fixed point; Projection; Viscosity approximation
nonexpansive mapping; iterative method; variational inequality
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/155083
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