Continuous dependence and fixed points for some multivalued operators

Abstract

In this paper we extend the notion of \(I^0\)-continuity and uniform \(I^0\)-continuity from [2] to set-valued operators. For families of such operators we prove (semi)continuity of the fixed point sets.

Keywords

• \(I^0\)-continuous multivalued operators
• Hausdorff-Pompeiu generalized semi-metric
• semi-continuous fixed point sets
• contractive operators