Algorithm for solving a new class of general mixed variational inequalities in Banach spaces

Authors:
Fu-Quan Xia;Nan-Jing Huang
Affiliations:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China;Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 3
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Abstract

In this paper, a new concept of @h-proximal mapping for a proper subdifferentiable functional (which may not be convex) on a Banach space is introduced. An existence and Lipschitz continuity of the @h-proximal mapping are proved. By using properties of the @h-proximal mapping, a new class of general mixed variational inequalities is introduced and studied in Banach spaces. An existence theorem of solutions is established and a new iterative algorithm for solving the general mixed variational inequality is suggested. A convergence criteria of the iterative sequence generated by the new algorithm is also given.