An example for a one-parameter nonexpansive semigroup

An Example for a One-parameter Nonexpansive Semigroup

(sg2) T(0)x = x for all x ∈ C; (sg3) T(s+ t) = T(s)◦T(t) for all s, t ≥ 0; (sg4) for each x ∈ C, the mapping t → T(t)x is continuous. We know that {T(t) : t ≥ 0} has a common fixed point under the assumption that C is weakly compact convex and E has the Opial property; see [3, 4, 5, 6, 8, 10, 12] and other works. Convergence theorems for one-parameter nonexpansive semigroups are proved in [1, 2...

Convergence theorems for semigroup of asymptotically nonexpansive mappings

In this paper, we prove the following results: Let K be a closed convex subset of a real Banach space E. Let T := {T (t) | t ∈ R+} be strongly continuous semigroup of asymptotically nonexpansive mappings from K into K such that F (T ) := ∩t∈R+F (T (t)) 6= ∅, where F (T (t)) = {x ∈ K |T (t)x = x} and R+ denotes the set of nonnegative real numbers. Then for arbitrary x0 ∈ K, the implicit iteratio...

The Set of Common Fixed Points of a One-parameter Continuous Semigroup of Mappings

In this paper, we prove the following theorem: Let {T (t) : t ≥ 0} be a one-parameter continuous semigroup of mappings on a subset C of a Banach space E. The set of fixed points of T (t) is denoted by F (

A New Example of a Minimal Nonfinitely Based Semigroup

Only three of the 15 973 distinct six-element semigroups are presently known to be nonfinitely based. This paper introduces a fourth example. 2010 Mathematics subject classification: primary 20M07.

A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions