A GENERAL ITERATIVE ALGORITHM FOR A FINITE FAMILY OF NONEXPANSIVE MAPPINGS IN A HILBERT SPACE
Sornsak Thianwan · Journal of applied mathematics & informatics · 2010
Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by arbitrarily chosen, , , where > 0, B : C H is a -inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient (0 is a projection of H onto C, A is a strongly positive linear bounded operator on H and is the W-mapping generated by a finite family of nonexpansive mappings , , , and {}, {}, , {}. Nonexpansivity of each ensures the nonexpansivity of . We prove that the sequence {} generated by the above iterative algorithm converges strongly to a common fixed point := which solves the variational inequality for all . Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.