A new iterative algorithm for solving a system of generalized mixed equilibrium problems for a kind of multi-valued nonlinear mappings

摘要

By using a new technique, namely, a specific way of choosing the indexes of the involved mappings, we introduce a new iterative algorithm for approximating common fixed points of a countable family of multi-valued totally quasi-φ-asymptotically nonexpansive mappings and obtain a strong convergence theorem under some suitable conditions. As application, an iterative solution to a system of generalized mixed equilibrium problems is studied. The results extend those of other authors, in which the involved mapping consists of just a single one.