Search results for: Jozef Myjak

Items from 1 to 11 out of 11 results

chapter

Markov Operators and Semifractals

Andrzej Lasota, Józef Myjak, Tomasz Szarek

Progress in Probability > Fractal Geometry and Stochastics III > Fractal Sets and Measures > 3-22

We show a relationship between the supports of invariant measures with respect to Markov operators and fractals and semifractals defined for Iterated Function Systems (or more generally for suitable multifunctions) without any use of probability theory.

article

Generic Existence and Approximation of Fixed Points for Nonexpansive Set-valued Maps

Francesco S. Blasi, Józef Myjak, Simeon Reich, Alexander J. Zaslavski

Set-Valued and Variational Analysis > 2009 > 17 > 1 > 97-112

We study nonexpansive set-valued maps in Banach and metric spaces. We are concerned, in particular, with the generic existence and approximation of fixed points, as well as with the structure of fixed point sets.

article

Reinforced walk on graphs and neural networks

Józef Myjak, Ryszard Rudnicki

Studia Mathematica > 2008 > 189 > 3 > 255-268

A directed-edge-reinforced random walk on graphs is considered. Criteria for the walk to end up in a limit cycle are given. Asymptotic stability of some neural networks is shown.

article

Stability of Random Dynamical Systems on Banach Spaces

Katarzyna Horbacz, Józef Myjak, Tomasz Szarek

Positivity > 2006 > 10 > 3 > 517-538

We consider a stochastic process generated by random dynamical systems on Banach spaces. Under the suitable assumptions we show that this process is weakly convergent to some limit.

article

On Stability of Some General Random Dynamical System

Katarzyna Horbacz, Józef Myjak, Tomasz Szarek

Journal of Statistical Physics > 2005 > 119 > 1-2 > 35-60

We consider a new random dynamical system which generalizes Markov processes corresponding to iterated function systems and Poisson driven stochastic differential equations. It can be used as a description of many physical and biological phenomena. Under the suitable assumption will be proved its stability.

article

Szpilrajn type theorem for concentration dimension

Jozef Myjak, Tomasz Szarek

Fundamenta Mathematicae > 2002 > 172 > 1 > 19-25

Let X be a locally compact, separable metric space. We prove that $dim_{T} X = inf{dim_{L} X': X' is homeomorphic to X}$, where $dim_{L} X$ and $dim_{T} X$ stand for the concentration dimension and the topological dimension of X, respectively.

article

Estimates of capacity of self-similar measures

Jozef Myjak, Tomasz Szarek

Annales Polonici Mathematici > 2002 > 78 > 2 > 141-157

We give lower and upper estimates of the capacity of self-similar measures generated by iterated function systems ${(S_i,p_i): i=1,...,N}$ where $S_i$ are bi-lipschitzean transformations.

article

A Lower Estimation of the Hausdorff Dimension for Attractors with Overlaps

Józef Myjak, Tomasz Szarek

Journal of Statistical Physics > 2001 > 105 > 3-4 > 649-657

We give a lower estimate of the Hausdorff dimension for attractors which can be obtained by an overlapping construction.

article

Box and Packing Dimensions of Typical Compact Sets

Jozef Myjak, Ryszard Rudnicki

Monatshefte für Mathematik > 2000 > 131 > 3 > 223-226

Abstract.Let (X,) be a complete metric space and let dim A be the upper box dimension of the set . We show that packing dimension of the typical (in the sense of Baire category) compact set is at least .

book

Orlicz type category theorems for functional and differential equations

Józef Myjak

Rozprawy Matematyczne

CONTENTSIntroduction.....................................................................................................................................5 1. General results.........................................................................................................................7 1.1. Residual sets......................................................................................

article

Boundary value problem for functional differential equations

Józef Myjak

Annales Polonici Mathematici > 1976 > 32 > 1 > 23-31

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