Misra, Prigogine and Courbage (MPC) demonstrated the possibility of obtaining stochastic Markov processes from deterministic dynamics simply through a ”change of representation” which involves no loss of information provided the dynamical system under consideration has a suitably high degree of instability of motion. From a mathematical point of view, MPC theory is a theory of positivity preser...

In this paper we show that every power bounded operator weighted shift with commuting normal weights is similar to a contraction. As an application of this result, we reduce the problem whether every centered power bounded operator is similar to a contraction to the analogous question about quasi-invertible centered operators.

In this paper, we define the concept of probabilistic like Menger (probabilistic like quasi Menger) space (briefly, PLM-space (PLqM-space)). We present some coupled fixed point and fixed point results for certain contraction type maps in partially order PLM-spaces (PLqM- spaces).

Metrics and more generally quasi-metrics are well krwwn in literature on domain theory and the semantics of programming languages. In this paper, we consider the role of quasi-metrics in defining abstract interpretations. ln fact these allow bot h to represent a notion of approximation together witll the error introduced, and to apply, under suitable conditions, Danach's contraction principle.

In this paper, we introduce the notion of weak $psi$-quasi contraction in generalized metric spaces and using this notion we obtain conditions for the existence of fixed points of a self map in $D$-complete generalized metric spaces. We deduce some corollaries from our result and provide examples in support of our main result.