10,759 research outputs found
Hyper-extensions in metric fixed point theory
We apply a modern axiomatic system of nonstandard analysis in metric fixed
point theory. In particular, we formulate a nonstandard iteration scheme for
nonexpansive mappings and present a nonstandard approach to fixed-point
problems in direct sums of Banach spaces.Comment: 12 page
TOPOLOGICALLY CONVEX SETS AND FIXED POINT THEORY
Topologically convex sets and fixed point theory - mappin
New directions in Nielsen-Reidemeister theory
The purpose of this expository paper is to present new directions in the
classical Nielsen-Reidemeister fixed point theory. We describe twisted
Burnside-Frobenius theorem, groups with \emph{property} and a
connection between Nielsen fixed point theory and symplectic Floer homology.Comment: 50 pages, surve
Proof mining in metric fixed point theory and ergodic theory
In this survey we present some recent applications of proof mining to the
fixed point theory of (asymptotically) nonexpansive mappings and to the
metastability (in the sense of Terence Tao) of ergodic averages in uniformly
convex Banach spaces.Comment: appeared as OWP 2009-05, Oberwolfach Preprints; 71 page
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