A general iterative method for nonexpansive mappings in Hilbert spaces |
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| Authors: | Giuseppe Marino |
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| Affiliation: | a Dipartimento di Matematica, Universita della Calabria, 87036 Arcavacata di Rende (Cs), Italy
b School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa |
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| 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  . Let  . 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  which solves the variational inequality  for x∈Fix(T). |
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| Keywords: | Nonexpansive mapping Iterative method Variational inequality Fixed point Projection Viscosity approximation |
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