Strong Convergence of a Generalized Iterative Method for Semigroups of Nonexpansive Mappings in Hilbert Spaces
Faculty of Mathematical Sciences, University of Tabriz, Tabriz 51664, Iran
Fixed Point Theory and Applications 2010, 2010:907275 doi:10.1155/2010/907275Published: 8 July 2010
Using -strongly accretive and -strictly pseudocontractive mapping, we introduce a general iterative method for finding a common fixed point of a semigroup of non-expansive mappings in a Hilbert space, with respect to a sequence of left regular means defined on an appropriate space of bounded real-valued functions of the semigroup. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality.