Invariant means and reversible semigroup of relatively nonexpansive mappings in Banach spaces (Q1724761)

Summary: The purpose of this paper is to study modified Halpern type and Ishikawa type iteration for a semigroup of relatively nonexpansive mappings \(\mathfrak{I} = \{T(s) : s \in S \}\) on a nonempty closed convex subset \(C\) of a Banach space with respect to a sequence of asymptotically left invariant means \(\{\mu_n \}\) defined on an appropriate invariant subspace of \(l^{\infty}(S)\), where \(S\) is a semigroup. We prove that, given some mild conditions, we can generate iterative sequences which converge strongly to a common element of the set of fixed points \(F(\mathfrak{I})\), where \(F(\mathfrak{I}) = \bigcap \{F(T(s)) : s \in S \}\).