A Remark on Recent Results for Finding Zeroes of Accretive Operators

In this paper we deal with methods for finding zeroes of set-valued operators A in Banach spaces. The first aim of this note is to show that the Yosida regularization may be combined with the schemes in [1, 2] keeping the strong convergence properties of the iterates and extending to set-valued operators two recent results by Chidume [1] and Chidume and Zegeye [2]. The second goal of the note is to make the connection with the iterative method studied in Benavides et al. [3]. This permits to obtain two convergence results under weaker conditions on the underlying operator. Let X be a real Banach space, a (possibly multivalued) operator A with domain D(A) and rangeR(A) inX is called accretive if, for each xi ∈D(A) and yi ∈A(xi) (i= 1,2), there is j ∈ J(x1− x2) such that 〈y1− y2, j〉 ≥ 0, where J stands for the normalized duality map on X , namely,