Variants of the New Caristi Theorem

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

Kaynakça

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