Characterization of ∑-Semicompleteness via Caristi’s Fixed Point Theorem in Semimetric Spaces

الملخص EN

Introducing the concept of ∑-semicompleteness in semimetric spaces, we extend Caristi’s fixed point theorem to ∑-semicomplete semimetric spaces.

Via this extension, we characterize ∑-semicompleteness.

We also give generalizations of the Banach contraction principle.