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Bull. Korean Math. Soc. 2011; 48(5): 991-1002
Printed September 1, 2011
https://doi.org/10.4134/BKMS.2011.48.5.991
Copyright © The Korean Mathematical Society.
An iteration schemes for nonexpansive mappings and variational inequalities
Hongjun Wang and Yisheng Song
Henan Normal University, Henan Normal University
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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