Generalized split feasibility problem governed by widely more generalized hybrid mappings in Hilbert spaces

Abstract

Generalized split feasibility problem governed by a widely more generalized hybrid mapping is studied. In particular, strong convergence of this algorithm is proved. As tools, resolvents of maximal monotone operators are technically maneuvered to facilitate the argument of the proof to the main result. Applications to iteration methods for various nonlinear mappings and to equilibrium problem are included.