Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces

Abstract EN

The purpose of this paper is to study modified Halpern type and Ishikawa type iteration for a semigroup of relatively nonexpansive mappings I = { T ( s ) : s ∈ S } on a nonempty closed convex subset C of a Banach space with respect to a sequence of asymptotically left invariant means { μ n } defined on an appropriate invariant subspace of l ∞ ( 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 ( I ) , where F ( I ) = ⋂ { F ( T ( s ) ) : s ∈ S } .