Some random fixed point theorems in generalized convex metric space (Q2812334)

Let \(K\) be a closed convex subset of a generalized convex metric space \((X,d)\), \((\Omega ,\Sigma )\) a measurable space, and \(T_i :\Omega \times K\to K\), \(i\in J\), a finite family of random mappings. The authors assume that the set \(F\) of common random fixed points of these mappings is nonempty and introduce a general, rather complicated, iteration process for the approximation of elements of \(F\). Let \(\{ \xi _n\}\) be a sequence obtained by this process. The main result of the paper says that, if \(T_i\) are uniformly quasi-Lipschitzian random mappings and \(\liminf_{n\to\infty} d(\xi _n(\omega ),F)=0\), then \(\xi _n\) converges to a common random fixed point.NEWLINENEWLINEReviewer's remark: It is not clear what the authors mean by the distance in the above condition. Here, \(F\) is the set of measurable functions from \(\Omega \) to \(K\), and they did not introduce any metric on such a space.