Equivalency of convergence between one-step iteration algorithm and two-step iteration algorithm of variational inclusions for HH-monotone mappings

The aim of this paper is to establish the equivalence of convergence for HH-monotone mappings of variational inclusions between the one-step iteration algorithm of the paper [Y.P. Fang, N.J. Huang, HH-monotone opertor and resolvent operator technique for variational inclusions, Appl. Math. Comput. 145 (2003) 795–803] and the two-step iteration algorithm of the paper [L.C. Zeng, S.M. Guu, J.C. Yao, Characterization of HH-monotone operators with applications to variational inclusions, Comput. Math. Appl. 50 (2005) 329–337]. It is clear from this paper that the one-step iteration algorithm with easy implement and small computational workload has more advantages than the two-step iteration algorithm.