  In this paper the stability and the perturbation bounds of Markov operators
acting on abstract state spaces are investigated. Here, an abstract state space
is an ordered Banach space where the norm has an additivity property on the
cone of positive elements. We basically study uniform ergodic properties of
Markov operators by means of so-called a generalized Dobrushin's ergodicity
coefficient. This allows us to get several convergence results with rates. Some
results on quasi-compactness of Markov operators are proved in terms of the
ergodicity coefficient. Furthermore, a characterization of uniformly
$P$-ergodic Markov operators is given which enable us to construct plenty
examples of such types of operators. The uniform mean ergodicity of Markov
operators is established in terms of the Dobrushin ergodicity coefficient. The
obtained results are even new in the classical and quantum settings
