Virtually nonexpansive maps and their convergence sets

Convergence of approximating fixed points sets for multivalued nonexpansive mappings

Let K be a closed convex subset of a Hilbert space H and T : K ⊸ K a nonexpansive multivalued map with a unique fixed point z such that {z} = T (z). It is shown that we can construct a sequence of approximating fixed points sets converging in the sense of Mosco to z.

Weak Convergence of Ishikawa Iterates for Nonexpansive Maps

We establish weak convergence of the Ishikawa iterates of nonexpansive maps under a variety of new control conditions and without employing any of the properties: (i) Opial’s property (ii) Fréchet differentiable norm (iii) Kadec-Klee property.

Nonexpansive Maps and Option Pricing

The famous Black-Sholes (BS) and Cox-Ross-Rubinstein (CRR) formulas are basic results in the modern theory of option pricing in financial mathematics. They are usually deduced by means of stochastic analysis; various generalisations of these formulas were proposed using more sophisticated stochastic models for common stocks pricing evolution. In this paper we develop systematically a determinis...

Special Moufang Sets, Their Root Groups and Their Μ-maps

We prove Timmesfeld’s conjecture that special abstract rank one groups are quasisimple. We show that in a special Moufang set the root groups are characterized on the one hand by being regular and normal in the point stabilizer, and on the other hand a normal transitive nilpotent subgroup of the point stabilizer is a root group. We prove that if a root group of a special Moufang set contains an...

Convergence to Compact Sets of Inexact Orbits of Nonexpansive Mappings in Banach and Metric Spaces