What does this research mean for the field?

The set of fixed points of an ascending correspondence with chain-complete values on a complete lattice is itself a complete lattice. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to prove that the set of fixed points for ascending correspondences on complete lattices forms a complete lattice.

March 6, 2026Economic TheoryOpen Access

Fixed point theorems for increasing correspondences on lattices

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The aim is to prove that the set of fixed points for ascending correspondences on complete lattices forms a complete lattice.
Utilized ascending correspondences defined from set X to its power set
Established conditions for chain-completeness on complete lattices
Generalized existing theorems to expand the understanding of fixed points
Proved that the fixed point set of ascending correspondences is indeed a complete lattice
Generalized Zhou's fixed point theorem for practical applications
Applied findings to analyze games with strategic complementarities

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Implication

This research demonstrates that fixed points form a complete lattice in certain mathematical structures, suggesting broader applications in economics.

Cite This Study

Lu YU (2026) studied this question.

synapsesocial.com/papers/69aa701a531e4c4a9ff5986b https://doi.org/10.1007/s00199-026-01702-7

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Implication

This research demonstrates that fixed points form a complete lattice in certain mathematical structures, suggesting broader applications in economics.

Fixed point theorems for increasing correspondences on lattices

Key Points

Discussion

Implication

Cite This Study

Fixed point theorems for increasing correspondences on lattices

Key Points

Discussion

Implication

Cite This Study

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