A general iterative method for nonexpansive mappings in Hilbert spaces
- Marino, Giuseppe
- Xu, Hong-Kun
DOIAbstract
AbstractLet 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)Txn+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)
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