A family of probability measures on the unit ball in R generates a family of generalized Steiner (GS-)points for every convex compact set in R. Such a ”rich” family of probability measures determines a representation of a convex compact set by GS-points. In this way, a representation of a setvalued map with convex compact images is constructed by GS-selections (which are defined by the GS-point...

in this paper. (1) we determine the complex-valued solutions of the following variant of van vleck's functional equation $$int_{s}f(sigma(y)xt)dmu(t)-int_{s}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin s,$$ where $s$ is a semigroup, $sigma$ is an involutive morphism of $s$, and $mu$ is a complex measure that is linear combinations of dirac measures $(delta_{z_{i}})_{iin i}$, such that for all $iin i$,...

We use cross ratios to describe second real continuous bounded cohomology for locally compact σ-compact topological groups. We also investigate the second continuous bounded cohomology group of a closed subgroup of the isometry group Iso(X) of a proper hyperbolic geodesic metric space X and derive some rigidity results for Iso(X)-valued cocycles.

We proved that a finite commuting Boyd-Wong type contractive family with equicontinuous words have the approximate common fixed point property. We also proved that given X Ă R, compact and convex subset, F : X Ñ X a compact-and-convex valued Lipschitz correspondence and g an isometry on X, then gF “ F g implies F admits a Lipschitz selection commuting with g.

We develop a domain-theoretic computational model for multi-variable differential calculus, which for the first time gives rise to data types for piecewise differentiable or more generally Lipschitz functions, by constructing an effectively given continuous Scott domain for real-valued Lipschitz functions on finite dimensional Euclidean spaces. The model for real-valued Lipschitz functions of n...

In topological fixed point theory, the Reidemeister trace is an invariant associated to a selfmap of polyhedron which combines information from Lefschetz and Nielsen numbers. this paper we define in context n-valued selfmaps compact polyhedra. We prove several properties generalize single-valued averaging formula.

A subset X of a real Hilbert space H is said to be proximally smooth provided that the function d X : H ! R (the distance to X) is continuously diierentiable on an open tube U around X. It is proven that this property is equivalent to d X having a nonempty proximal subgradient at every point of U, and that the (G^ ateaux = Fr echet) derivative is locally Lipschitz on U. The Lipschitz behavior o...

Let X be a compact Hausdorff space, and let {Ax : x ∈ X} {Bx collections of Banach algebras such that each Ax is Bx-bimodule. Using the theory bundles spaces as tool, we investigate module amenability certain Ax-valued functions on over Bx-valued X.

An ordinary differential equation x = f (t, x(t)) (ODE) uniquely assigns the time derivative x (t) = d dt x(t) as a function of t and x. A differential inclusion x ∈ F (t, x(t)), (DI) on the other hand, only requires that the derivative x be inside a given set F (t, x) ⊂ R n. Therefore, given an initial condition x(0) = ¯ x, one can usually find several solutions of (DI). f(x) x _ x _ x x F(x) ...