Hyers-Ulam-Rassias stability of the Apollonius type quadratic mapping in RN-spaces.
The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance introduced by Dolbeault and Ławrynowicz (1989) in connection with bordered holomorphic chains of dimension one. Several properties of the related hyperbolic-like manifolds are considered remarking the analogies with and differences from the familiar hyperbolic and Stein manifolds. Likewise several examples are treated in detail.
Extending previous results of H. Salas we obtain a characterisation of hypercyclic weighted shifts on an arbitrary F-sequence space in which the canonical unit vectors form a Schauder basis. If the basis is unconditional we give a characterisation of those hypercyclic weighted shifts that are even chaotic.
Let X be an infinite dimensional separable Banach space. There exists a hypercyclic operator on X which is equal to the identity operator on an infinite dimensional closed subspace of X.
In this paper we use Nachbin’s holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables