Extensions of Virtual Stability

Abstract

We present the notion of xed point iteration schemes, which includes concepts of various iteration processes. Then we extend the concept of virtually stable maps to virtually stable schemes. This gives a retraction result inducing contractibility criterion for xed point sets of some self-maps and set-valued maps of nonexpansive type. Moreover, we present a sequence of self-maps, which is not a xed point iteration scheme but induces a retraction result similar to virtually stable schemes, called a xed point resolution.