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An Implicit Hierarchical Fixed-Point Approach to General Variational Inequalities in Hilbert Spaces

Abstract

Let be a nonempty closed convex subset of a real Hilbert space . Let be a -Lipschitzian and -strongly monotone operator with constants , be nonexpansive mappings with where denotes the fixed-point set of , and be a -contraction with coefficient . Let and , where . For each , let be a unique solution of the fixed-point equation . We derive the following conclusions on the behavior of the net along the curve : (i) if , as , then strongly, which is the unique solution of the variational inequality of finding such that and (ii) if , as , then strongly, which is the unique solution of some hierarchical variational inequality problem.

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Correspondence to Ching-Feng Wen.

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Zeng, L., Wen, C. & Yao, J. An Implicit Hierarchical Fixed-Point Approach to General Variational Inequalities in Hilbert Spaces. Fixed Point Theory Appl 2011, 748918 (2011). https://doi.org/10.1155/2011/748918

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Keywords

  • Hilbert Space
  • General Variational
  • Variational Inequality
  • Differential Geometry
  • Computational Biology