%0 Journal Article
%T Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space
%A Manaka
%A Hiroko
%A Takahashi
%A Wataru
%J Cubo (Temuco)
%D 2011
%I Scientific Electronic Library Online
%R 10.4067/S0719-06462011000100002
%X let c be a closed convex subset of a real hilbert space h. let t be a nonspreading mapping of c into itself, let a be an ¦Á-inverse strongly monotone mapping of c into h and let b be a maximal monotone operator on h such that the domain of b is included in c. we introduce an iterative sequence of finding a point of f(t)¡É(a+b)-10, where f(t) is the set of fixed points of t and (a + b)-10 is the set of zero points of a + b. then, we obtain the main result which is related to the weak convergence of the sequence. using this result, we get a weak convergence theorem for finding a common fixed point of a nonspreading mapping and a nonexpansive mapping in a hilbert space. further, we consider the problem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonspreading mapping.
%K nonspreading mapping
%K maximal monotone operator
%K inverse strongly-monotone mapping
%K fixed point
%K iteration procedure.
%U http://www.scielo.cl/scielo.php?script=sci_abstract&pid=S0719-06462011000100002&lng=en&nrm=iso&tlng=en