SET-VALUED FIXED POINT THEOREM BASED ON THE SUPER-TRAJECTORY IN COMPLETE SUPER HAUSDORFF METRIC SPACE

Abstract

In this paper, a super Hausdorff metric is introduced and constructed, and the completeness of super Hausdorff metric space is studied. A new concept, the trajectory of set valued mapping is introduced, and by using the trajectory condition, the existence theorems for the set-valued fixed point and the fixed point of a new class of set valued mappings is proved. The obtained results seem to be general in nature.