On the stability of finding approximate fixed points by simplicial methods

Abstract

Abstract This paper reports some new results in relation to simplicial algorithms considering continuities of approximate fixed point sets. The upper semi-continuity of a set-valued mapping of approximate fixed points using vector-valued simplicial methods is proved, and thus one obtains the existence of finite essential connected components in approximate fixed point sets by vector-valued labels; examples are given to show that this is very different from the property for integer-valued labeling simplicial methods. The existence of essential sets is also proved focusing on both perturbations of domains and functions.

Keywords

• stability
• approximate fixed point
• simplex