Olawale Kazeem Oyewole, Alexander J. Zaslavski, and Simeon Reich
A Fixed Point Theorem in Length Spaces
Dynamic Systems and Applications 31 (2022) 173-180

https://doi.org/10.46719/dsa202231.03.02

ABSTRACT.
Let K be a closed subset of a complete metric space X and let CB(X) denote the family of all nonempty, closed and bounded subsets of X. Assuming further that X is a length space, we establish a fixed point theorem for those strictly contractive set-valued mappings F : K → CB(X), for which the image of each point on the boundary of K is a subset of K.

AMS (MOS) Subject Classification. 47H10, 54H25.
Key Words and Phrases. Fixed point, length space, metric space, set-valued mapping, strict
contraction.