No abstract

In this paper, we establish several random fixed point theorems for random operators satisfying some iterative condition w.r.t. a measure of noncompactness. We also discuss the case of monotone random operators in ordered Banach spaces. Our results extend several earlier works, including Itoh’s random fixed point theorem. As an application, we discuss the existence of random solutions to a class of random first-order vector-valued ordinary differential equations with lack of compactness.

In this paper, we show the existence of random mild solutions for a broad class of random integrodifferential equations with lack of compactness. The results are obtained using noncompact resolvent operators and a fixed point theorem of Monch type. Our results are applied to a large variety of partial differential equations in which memory effects are considered. Some examples are provided to illustrate the theoretical results. Mathematics Subject Classification (2010). Primary 45K05, 47G20, 47D06, 47H10; Secondary 47H08.