Fixed Point Theorems for Monotone Mappings in Ordered Banach Spaces Under Weak Topology Features

We present several fixed point theorems for monotone nonlinear operators in ordered Banach spaces. The main assumptions of our results are formulated in terms of the weak topology. As an application, we study the existence of solutions to a class of first-order vector-valued ordinary differential equations. Our conclusions generalize many well-known results.

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