2014•arXiv (Cornell University)Open access
Strong convergence with a modified iterative projection method for\n hierarchical fixed point problems and variational inequalities
İbrahim Karahan, Murat Özdemir
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Abstract
This paper deals with a modified iterative projection method for\napproximating a solution of the hierarchical fixed point problem for a sequene\nof nearly nonexpansive mappings with respect to a nonexpansive mapping. It is\nshown that under certain approximate assumptions on the operators and\nparameters, the modified iterative sequence converges strongly to a common\nelement of the set of the common fixed points of nearly nonexpansive\nmappings.Also, this point solves some variational inequality. As a special\ncase, this projection method can be used to find the minimum norm solution of\nthe given variational inequality. The results here improve and extend some\nrecent corresponding results of other authors.\n
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