Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces

摘要

We study a strong convergence for a common fixed point of afinite family of quasi-Bregman nonexpansive mappings in the framework ofreal reflexive Banach spaces. As a consequence, convergence for a commonfixed point of a finite family of Bergman relatively nonexpansive mappings isdiscussed. Furthermore, we apply our method to prove strong convergence theoremsof iterative algorithms for finding a common solution of a finite familyequilibrium problem and a common zero of a finite family of maximal monotonemappings. Our theorems improve and unify most of the results that havebeen proved for this important class of nonlinear mappings.