Applications of the Best Approximation Operator to *-Nonexpansive Maps in Hilbert Spaces
Nawab Hussain, Abdul Rahim Khan · Numerical Functional Analysis and Optimization · 2003
The notion of a *-nonexpansive multivalued map is different from that of a continuous map. We give some Ky Fan type best approximation theorems for *-nonexpansive mappings defined on closed convex unbounded subsets of a Hilbert space. As applications of our theorems, we derive fixed point results under many boundary conditions. Approximating sequences to the fixed points are also constructed.