A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings
© C. Klin-eam and S. Suantai 2009
Received: 3 June 2009
Accepted: 1 November 2009
Published: 4 November 2009
A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational inequalities. Moreover, we apply our main result to obtain strong convergence to a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping in a Hilbert space.
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