Modified hybrid steepest-descent methods for variational inequalities and fixed points

作者：Saeidi Shahram^*

来源：Mathematical and Computer Modelling, 2010, 52(1-2): 134-142.

DOI：10.1016/j.mcm.2010.01.023

• Common fixed point
• Equilibrium problem
• Hybrid steepest-descent method
• Iterative algorithm
• Nonexpansive mapping
• Variational inequality

Assume that C is a nonempty closed convex subset of a Hilbert space H and B : C -> H is a strongly monotone mapping. Assume also that F is the intersection of the common fixed points of an infinite family of nonexpansive mappings on C and the set of solutions of a system of equilibrium problems. We devise a modified hybrid steepest-descent method which generates a sequence (x(n)) from an arbitrary initial point x(0) is an element of H. The sequence (x(n)) is shown to converge in norm to the unique solution of the variational inequality VI(B, F) under suitable conditions.

• 出版日期2010-7