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The work of professor Andrzej Lasota on asymptotic stability and recent progress

Bartoszek W.

Opuscula Mathematica

2008

Vol. 28, no. 4

395-413

The paper is devoted to Professor Andrzej Lasota's contribution to the ergodic theory of stochastic operators. We have selected some of his important papers and shown their influence on the evolution of this topic. We emphasize the role A. Lasota played in promoting abstract mathematical theories by showing their applications. The article is focused exclusively on ergodic properties of discrete stochastic semigroups {Pn : n ≥ 0}. Nevertheless, almost all of Lasota's results presented here have their one-parameter continuous semigroup analogs.

On the recursive sequence Xn+1=alfa+Xn-k:f(Xn,....Xn-k+1)

Karakostas G., Stevic S.

Demonstratio Mathematica

2005

Vol. 38, nr 3

595-610

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the nonnegative solutions of the difference equation of the form Xn+l=alfa+Xn-k:f(Xn,....Xn-k+1, n=0, 1, ..... is investigated, where alfa > 0, k is an element of N and f : [0,infinity)- (0,infinity)k is a continuous function nondecreasing in each variable.