Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces
Tomonari Suzuki · Fixed Point Theory and Applications · 2006
Abstract We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let "Equation missing" be a bounded closed convex subset of a uniformly smooth Banach space "Equation missing". Let "Equation missing" be an infinite family of commuting nonexpansive mappings on "Equation missing". Let "Equation missing" and "Equation missing" be sequences in "Equation missing" satisfying "Equation missing" for "Equation missing". Fix "Equation missing" and define a sequence "Equation missing" in "Equation missing" by "Equation missing" for "Equation missing". Then "Equation missing" converges strongly to "Equation missing", where "Equation missing" is the unique sunny nonexpansive retraction from "Equation missing" onto "Equation missing".