Journal of Differential Equations vol. 159, no. 2, pp. 307 - 320
Indexed
SCI; SCIE; SCOPUS
Document Type
Article
Abstract
Let T be a nonexpansive self-mapping of C where C is a nonempty closed convex subset of a Banach space E. We define T λ for 0<λ<1 by T λ=λT+(1-λ)I, where I is the identity operator on C, and denote x n=T n λx 0 where x 0∈C. Then the related initial value problem is du/dt=-(I-T)u(t) with u(0)=x 0∈C. The facts that
x n-Tx n
=O(1/n) as n→∞ and
u′(t)
=O(1/t) as t→∞ are known when C is bounded. In this paper we look for a rate of asymptotic regularity for
if
u(t)
=O(t α) where 0≤α≤1. We prove
=O(t -β) as t→∞, where α+2β=1 and obtain an estimate on