Journal of Inequalities and Applications (Oct 2017)

Implicit and explicit iterative algorithms for hierarchical variational inequality in uniformly smooth Banach spaces

  • Lu-Chuan Ceng,
  • Yung-Yih Lur,
  • Ching-Feng Wen

DOI
https://doi.org/10.1186/s13660-017-1523-8
Journal volume & issue
Vol. 2017, no. 1
pp. 1 – 25

Abstract

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Abstract The purpose of this paper is to solve the hierarchical variational inequality with the constraint of a general system of variational inequalities in a uniformly convex and 2-uniformly smooth Banach space. We introduce implicit and explicit iterative algorithms which converge strongly to a unique solution of the hierarchical variational inequality problem. Our results improve and extend the corresponding results announced by some authors.

Keywords