Assume that is a closed convex subset of a uniformly convex Banach space , and assume that is a nonexpansive semigroup on . By using the following implicit iteration sequence defined by the main purpose of this paper is to establish a weak convergence theorem for the nonexpansive semigroup in uniformly convex Banach spaces without the Opial property. Our results are different from some recently announced results.
"On the weak convergence theorem for nonexpansive semigroups in Banach spaces." Ann. Funct. Anal. 8 (3) 341 - 349, August 2017. https://doi.org/10.1215/20088752-0000018X