Several classes of hereditarily normal spaces are characterized in terms of extending upper semi-continuous compact-valued mappings. The case of controlled extensions is considered as well. Applications are obtained for real-valued semi-continuous functions.

INTrODUCTION Recurrent neural networks whose neurons are fully interconnected have been utilized to implement associative memories and solve optimization problems. These networks are regarded as nonlinear dynamical feedback systems. Stability properties of this class of dynamical networks are an important issue from applications point of view. ABSTrACT Global stability analysis for complex-valu...

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.

Let Sβ := {z ∈ C : | Im z| < β} be a strip in the complex plane. For fixed integer r ≥ 0 let Hr ∞,β denote the class of 2π-periodic functions f , which are analytic in Sβ and satisfy |f(r)(z)| ≤ 1 in Sβ . Denote by Hr,R ∞,β the subset of functions from Hr ∞,β that are real-valued on the real axis. Given a function f ∈ Hr ∞,β , we try to recover f(ζ) at a fixed point ζ ∈ R by an algorithm A on t...

Two refractory problems in modern constructive analysis concern real-valued functions on the closed unit interval: Is every function pointwise continuous? Is every pointwise continuous function uniformly continuous? For monotone functions, some answers are given here. Functions which satisfy a certain strong monotonicity condition, and approximate intermediate values, are pointwise continuous. ...