Summary: We note that the main convergence theorem in [C.-J. Zhang
, J.-L. Li
and B.-Q. Liu
, Comput. Math. Appl. 61, No. 2, 262–276 (2011; Zbl 1211.65063
)] is incorrect and we prove a correction. We also modify Halpern’s iteration for finding a fixed point of a strongly relatively nonexpansive mapping in a Banach space. Consequently, two strong convergence theorems for a relatively nonexpansive mapping and for a mapping of firmly nonexpansive type are deduced. Using the concept of duality theorems, we obtain analogous results for strongly generalized nonexpansive mappings and for mappings of firmly generalized nonexpansive type. In addition, we study two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a Banach space.