Variants of the New Caristi Theorem

Year 2023, , 348 - 361, 23.07.2023

Sehie Park

https://doi.org/10.31197/atnaa.1290064

Abstract

The well-known Caristi fixed point theorem has numerous generalizations and modifications. Recently there
have appeared its equivalent dual forms and generalizations based on new concept of lower semicontinuity
from above by several authors. In the present article, we give new proofs of such new versions and their
equivalent formulations by applying our Metatheorem in the ordered fixed point theory.

Keywords

Caristi, Ekeland, fixed point, preorder, metric space, stationary point, maximal element, lower semicontinuity from above

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