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

Authors:
Shahram Saeidi
Affiliations:
Department of Mathematics, University of Kurdistan, Sanandaj 416, Kurdistan, Iran
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2010

Citing 1
Cited 1

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Strong convergence for a minimization problem on solutions of systems of equilibrium problems and common fixed points of an infinite family and semigroup of nonexpansive mappings

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Abstract

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@?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.