Random fixed point theorem in generalized Banach space and applications (Q289607)

In this paper, the authors present some number of random fixed point theorems in so-called generalized Banach spaces and their applications to systems of random differential equations with initial or boundary conditions. The paper consists of an introduction (containing a lot of information on generalized metric spaces, random operators and random fixed points), random versions of the Perov, Schauder and Krasnosielski results, and interesting applications of these results to a random Cauchy problem for a system of two first order differential equations as well as a second order boundary value problem for a system of two random differential equations.NEWLINENEWLINEAlthough there are some misprints (e.g., the definition of vector-valued metric, which is rather called a dislocated metric; Pervo instead of Perov; in the Definition 2.5, I hope it is natural to assume that \(M\) has nonnegative elements), the paper is very interesting both for those working in theory and applications of functional analysis to random differential equations.