Visco-resolvent algorithms for monotone operators and nonexpansive mappings

Two new type of visco-resolvent algorithms for nding a zero of the sum of two monotone operators and a xed point of a nonexpansive mapping in a Hilbert space are investigated. The algorithms consist of the zeros and the xed points of the considered problems in which one operator is replaced with its resolvent and a viscosity term is added. Strong convergence of the algorithms are shown. As special cases, we can approach to the minimum norm common element of the zero of the sum of two monotone operators and the xed point of a nonexpansive mapping without using the metric projection. Some applications are included.