An iteration schemes for nonexpansive mappings and variational inequalities
Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 991-1002
https://doi.org/10.4134/BKMS.2011.48.5.991
Printed September 1, 2011
Hongjun Wang and Yisheng Song
Henan Normal University, Henan Normal University
Abstract : An iterative algorithm is provided to find a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of some variational inequality in a Hilbert space. Using this result, we consider a strong convergence result for finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping. Our results include the previous results as special cases and can be viewed as an improvement and refinement of the previously known results.
Keywords : metric projection, inverse-strongly monotone mapping, nonexpansive mapping, variational inequality, strong convergence
MSC numbers : 47H06, 47J05, 47J25, 47H10, 47H17
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