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lower semicontinuous function

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lower semicontinuous function [¦lō·ər ‚sem·ē·kən′tin·yə·wəs ‚fənk·shən]
(mathematics)
A real-valued function ƒ(x) is lower semicontinuous at a pointx0if, for any small positive number ε, ƒ(x) is always greater that ƒ(x0) - ε for allxin some neighborhood ofx0.


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1) where f : E [right arrow] E is a self mapping and [phi] : [0, + [infinity]) [right arrow] [0, + [infinity]) is a lower semicontinuous function from right such that [phi] is positive on (0, + [infinity]) and [phi](0) = 0.
 
 
 
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