Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840680 | Nonlinear Analysis: Theory, Methods & Applications | 2011 | 5 Pages |
Abstract
Let XX be a normed space and TT and II be two nonexpansive self-maps on the closed convex subset C⊂XC⊂X. It is proved that if (I,T)(I,T) is a Banach operator pair and T(C)¯ is compact then F(I,T)≠0̸F(I,T)≠0̸. A family of nonexpansive maps is also investigated; the well-known De Marr’s fixed point theorem is extended to the noncommuting case by introducing a notion of Banach operator family. As an application of the theorem, the problem for the common fixed point in invariant approximation for convex set is solved directly in a quite different way from the others before.
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Authors
Jianren Chen, Zhongkai Li,