Markov operators acting on Polish spaces
We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.
Maximal distributional chaos of weighted shift operators on Köthe sequence spaces
During the last ten some years, many research works were devoted to the chaotic behavior of the weighted shift operator on the Köthe sequence space. In this note, a sufficient condition ensuring that the weighted shift operator defined on the Köthe sequence space exhibits distributional -chaos for any and any is obtained. Under this assumption, the principal measure of is equal to 1. In particular, every Devaney chaotic shift operator exhibits distributional -chaos for any .
Maximal scrambled sets for simple chaotic functions.
This paper is a continuation of [1], where a explicit description of the scrambled sets of weakly unimodal functions of type 2∞ was given. Its aim is to show that, for an appropriate non-trivial subset of the above family of functions, this description can be made in a much more effective and informative way.
Meromorphic functions whose Julia sets contain a free Jordan arc.
Monotonous stability for neutral fixed points.
Nonlinear contractive conditions: A comparison and related problems
We establish five theorems giving lists of nonlinear contractive conditions which turn out to be mutually equivalent. We derive them from some general lemmas concerning subsets of the plane which may be applied both in the single- or set-valued case as well as for a family of mappings. A separation theorem for concave functions is proved as an auxiliary result. Also, we discuss briefly the following problems for several classes of contractions: stability of procedure of successive approximations,...
Nonlinear functional equations and their Baire category properties.
Normalization of almost conformal parabolic germs.
Note on commutable functions.
Note on the existence of iteration groups
Note on the local growth of iterated polynomials.
Note relative à l'approximation des moyennes géométriques par des séries de moyennes arithmétiques et de moyennes harmoniques
On a Functional Equation Related to Iteration.
On a generalized Dhombres functional equation. II.
We consider the functional equation where is a given increasing homeomorphism of an open interval and is an unknown continuous function. In a previous paper we proved that no continuous solution can cross the line where is a fixed point of , with a possible exception for . The range of any non-constant continuous solution is an interval whose end-points are fixed by and which contains in its interior no fixed point except for . We also gave a characterization of the class of continuous...
On a problem of V. Pták
On a system of functional equations.
On a theorem of B. Barna.
On an equation of linear iteration.
On certain iterative sequences
On common fixed and periodic points of commuting functions.