On the continuously essential components of fixed points for the set-valued mapping
Fan Xiao-dong · Basic Sciences Journal of Textile Universities · 2007
The method of essential solution has been widely used in various fields recently.It plays a crucial role in the study of stability of Nash equilibria,fixed point,etc.A further study on the stability is given.A concept of continuously essential sets of fixed points for upper semicontinuous mappings with nonempty,convex and compact values is introduced,and the existence of the continuously essential component is established.It is proved that there exist at least one minimal continuously essential set of fixed points,and the minimal continuously essential set is connected.