Heterogeneous vectorial fixed point theorems

In this paper we obtain fixed point theorems for operators defined on Cartesian product spaces under heterogeneous conditions upon the structure of the factor spaces and the operator components. The main results combine Banach-Perov contraction principle with topological fixed point theorems of Monch type in strong and weak topologies. The results make possible a tinted analysis of the operator systems. An application of the vectorial technique to evolution equations with nonlocal Cauchy conditions is included.