RANDOM HYBRID FIXED POINT THEOREMS FOR MONOTONE MAPPINGS IN PARTIALLY ORDERED POLISH SPACES WITH APPLICATIONS

Abstract

We present some random fixed point theorems for partially contractive and continuous random mappings in a partially ordered Polish space and apply them to prove the existence and uniqueness theorems for an initial and a periodic boundary value problem of first order nonlinear random differential equations under weaker monotonic conditions. Finally, random differential inequalities and comparison principles are also established for the considered differential equations.