Poisson equations associated with a homogeneous and monotone function: necessary and sufficient conditions for a solution in a weakly convex case

DOI10.1016/j.na.2009.12.010zbMath1215.47052OpenAlexW2084982707MaRDI QIDQ2267556

Rolando Cavazos-Cadena, Daniel Hernández-Hernández

Publication date: 1 March 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.12.010

zbMATH Keywords

eigenvalue problemgeneralized Perron-Frobenius theoremCollatz-Wielandt relationscommunication matrixminimal closed set

Mathematics Subject Classification ID

Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)

Related Items (5)

Unnamed Item ⋮ Contractive mappings and existence of cycle times for a monotone and homogeneous function ⋮ Equivalence of communication and projective boundedness properties for monotone and homogeneous functions ⋮ A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectors ⋮ Ergodicity conditions for zero-sum games

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized eigenvectors and sets of nonnegative matrices
• An extension of Morishima's nonlinear Perron-Frobenius theorem
• Necessary and sufficient conditions for a solution to the risk-sensitive Poisson equation on a finite state space
• Spectral theorem for convex monotone homogeneous maps, and ergodic control
• From max-plus algebra to nonexpansive mappings: A nonlinear theory for discrete event systems.
• Non-negative matrices and Markov chains.
• Iteration of order preserving subhomogeneous maps on a cone
• Hilbert’s projective metric and iterated nonlinear maps
• Iterated nonlinear maps and Hilbert’s projective metric. II
• Some Relations Between Nonexpansive and Order Preserving Mappings
• The Perron-Frobenius theorem for homogeneous, monotone functions
• On the dynamics of sup-norm non-expansive maps

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