Rajandra P. Pant, Rale M. Nikolic, Abhijit Pant, and Mahesh C. Joshi
A Caristi and Meir-Keeler Type Characterization of Completeness For Menger PM Spaces
Dynamic Systems and Applications 31 (2022) 181-193

https://doi.org/10.46719/dsa202231.03.03

ABSTRACT.
In this paper the Caristi fixed point theorem and a Meir-Keeler type fixed point theorem for Menger PM-spaces is generalized by employing a weaker form of continuity. We prove that these theorems characterize completeness of the Menger PM space as well as Cantor’s intersection property.

AMS (MOS) Subject Classification. 47H10, 54H25.
Key Words and Phrases. Menger PM-spaces; Fixed point; Weak orbital continuity; Contractive
mapping.