Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces

Abstract

Generalized split feasibility problems governed by generalized hybrid mappings are studied via iterative methods. Several algorithms are introduced to solve them. In particular, weak convergence of these algorithms is proved. As tools, averaged mappings and resolvents of maximal monotone operators are technically maneuvered to facilitate the argument of the proofs to the main results. Applications to Mann’s iteration method for nonexpansive mappings and to equilibrium problems are included.