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versión On-line ISSN 0719-0646


MANAKA, Hiroko  y  TAKAHASHI, Wataru. Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space. Cubo [online]. 2011, vol.13, n.1, pp.11-24. ISSN 0719-0646.

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.

Palabras clave : Nonspreading mapping; maximal monotone operator; inverse strongly-monotone mapping; fixed point; iteration procedure.

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