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Applications of the Best Approximation Operator to -Nonexpansive Maps in Hilbert Spaces
Journal article   Peer reviewed

Applications of the Best Approximation Operator to -Nonexpansive Maps in Hilbert Spaces

N. Hussain and A. R. Khan
Numerical functional analysis and optimization, Vol.24(3-4), pp.327-338
08/01/2003
DOI: https://doi.org/10.1081/NFA-120022926

Abstract

2000 AMS Subject Classification: 41A65 Best approximation Fixed point Hilbert space Nonexpansive map Weakly inward map
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.

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