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Research Article
 

The Fixed Points of Certain Discontinuous Operators on Locally Convex Spaces



J.O. Olaleru
 
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ABSTRACT

The fixed point properties of four classes of operators mapping a metrisable locally convex space into itself are considered. These classes include contraction and nonexpansive 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 generalise the results of Derrick and Nova from Banach spaces to metrisable locally convex spaces.

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  How to cite this article:

J.O. Olaleru , 2006. The Fixed Points of Certain Discontinuous Operators on Locally Convex Spaces. Journal of Applied Sciences, 6: 2813-2816.

DOI: 10.3923/jas.2006.2813.2816

URL: https://scialert.net/abstract/?doi=jas.2006.2813.2816

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