Visco-resolvent algorithms for monotone operators and nonexpansive mappings
Peize Li, Shin Min Kang, Li-Jun Zhu · The Journal of Nonlinear Sciences and Applications · 2014
Two new type of visco-resolvent algorithms for finding a zero of the sum of two monotone operators and a fixed point of a nonexpansive mapping in a Hilbert space are investigated. The algorithms consist of the zeros and the fixed 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 fixed point of a nonexpansive mapping without using the metric projection. Some applications are included.