Summary: S.-Y. Matsushita
and W. Takahashi
[J. Approx. Theory 134, No. 2, 257–266 (2005; Zbl 1071.47063
)] proved a strong convergence theorem for relatively nonexpansive mappings in a Banach space by using the hybrid method (
method) in mathematical programming. The purpose of this paper is to modify this method and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of our monotone CQ method is faster than the hybrid method of [op. cit.]. In addition, the Cauchy sequence method is used in this paper without using the Kadec-Klee property.