The Fixed Points of Certain Discontinuous Operator on Locally Convex Spaces
The fixed point properties of four classes of operators mapping a metrisable locally convex space into itself are considered. These classes include contraction, and non-expansive mappings, discontinuous operators for certain parameter values of the classes. The existence of fixed points are proved for these classes of mappings under some conditions. Furthermore, a cone ordering scheme is devised for one of these classes, while another is shown to have open mapping properties. All these results generalize the work of Derrick and Nova from Banach spaces to metrisable locally convex spaces.