An extension of Tarski's fixed point theorem and its application to isotone complementarity problems

DOI10.1007/BF02612716zbMath0526.90084MaRDI QIDQ3040946

Takao Fujimoto

Publication date: 1984

Published in: Mathematical Programming (Search for Journal in Brave)

zbMATH Keywords

set-valued mappingsTarski's fixed point theoremcomplete vector latticeisotone set-valued operators

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Fixed-point and coincidence theorems (topological aspects) (54H25) Programming in abstract spaces (90C48)

Related Items (26)

On strategic complementarities in discontinuous games with totally ordered strategies ⋮ Nonlinear Leontief models in abstract spaces ⋮ Fixed point theorems for monotone multi-valued mappings in partially ordered metric spaces ⋮ Order-preservation of solution correspondence for parametric generalized variational inequalities on Banach lattices ⋮ Inductive properties of fixed point sets of mappings on posets and on partially ordered topological spaces ⋮ The nonlinear Perron-Frobenius problem for set-valued maps in a closed convex cone in \(\mathbb{R}^ N\) ⋮ Order-preservation properties of resolvent operators and their applications to variational inequalities ⋮ Some hybrid fixed point theorems related to optimization ⋮ Solvability of Variational Inequalities on Hilbert Lattices ⋮ Remarks on monotone multivalued mappings on a metric space with a graph ⋮ The contraction principle for set valued mappings on a metric space with a graph ⋮ Unique Tarski Fixed Points ⋮ Browder type fixed point theorems and Nash equilibria in generalized games ⋮ Nonlinear operators in Euclidean spaces: An elementary `users guide' for economists ⋮ Optimal solutions to variational inequalities on Banach lattices ⋮ Kneser's theorem and the multivalued generalized order complementarity problem ⋮ Fixed Point Theorems for Discontinuous Maps on a Non‐convex Domain ⋮ Order-clustered fixed point theorems on chain-complete preordered sets and their applications to extended and generalized Nash equilibria ⋮ Several extensions of the Abian-Brown fixed point theorem and their applications to extended and generalized Nash equilibria on chain-complete posets ⋮ Applications of order-clustered fixed point theorems to generalized saddle point problems and preordered variational inequalities ⋮ A note on the relationship between the isotone assumption of the Abian-Brown fixed point theorem and Abian's most basic fixed point theorem ⋮ Monotone Relations, Fixed Points and Recursive Definitions ⋮ Upper order-preservation of the solution correspondence to vector equilibrium problems ⋮ Fixed points of multivalued mappings in modular function spaces with a graph ⋮ Applications of order-theoretic fixed point theorems to discontinuous quasi-equilibrium problems ⋮ Relation-algebraic computation of fixed points with applications

Cites Work

• A lattice-theoretical fixpoint theorem and its applications
• Equivalence of Linear Complementarity Problems and Linear Programs in Vector Lattice Hilbert Spaces
• Nonlinear Complementarity Problems in a Function Space
• Equivalence of Nonlinear Complementarity Problems and Least Element Problems in Banach Lattices
• A Least-Element Theory of Solving Linear Complementarity Problems as Linear Programs
• Unnamed Item

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