Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space

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 α-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)∩(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.