Some general principles in tropical convexities

Horvath, Charles D.; Serea, Oana Silvia; Briec, Walter

doi:10.1051/proc/201657048

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Max-plus Convexity In Archimedean Riesz Spaces With a Unit2

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“…Proof. From 3.0.12 in [19]. ✷ We conclude this section by showing that the max-plus metric is additive on max-plus segments, Proposition 1 below.…”

Section: Max-plus Convexity In Archimedean Riesz Spaces With a Unitmentioning

confidence: 77%

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Tropical convexity in Riesz spaces

Horvath

2017

Topology and its Applications

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We study max-plus convexity in an Archimedean Riesz space E with an order unit u; the definition of max-plus convex sets is algebraic and we do not assume that E has an a priori given topological structure. To the given unit u one can associate two equivalent norms · u and · hu on E; the distance D hu on E associated to · hu is a geodesic distance for which max-plus convex sets in E are geodesically closed sets. Under suitable assumptions, we establish max-plus versions of some fixed points and continuous selection theorems that are well known for linear convex sets and we show that hyperspaces of compact max-plus convex sets are Absolute Retracts.MSC: 14T99, 46A40, 54H25, 54C55, 54C65, 62P20.

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“…Proof. From 3.0.12 in [19]. ✷ We conclude this section by showing that the max-plus metric is additive on max-plus segments, Proposition 1 below.…”

Section: Max-plus Convexity In Archimedean Riesz Spaces With a Unitmentioning

confidence: 77%

“…The proof of Lemma 6 below is left to the reader; that of Lemma 7 can here be done by hand or one can go to Lemma 2.1.5 in [19]. Lemma 6.…”

Section: Max-plus Convexity In Archimedean Riesz Spaces With a Unitmentioning

confidence: 99%

Tropical convexity in Riesz spaces

Horvath

2017

Topology and its Applications

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Ky-Fan inequality, Nash equilibria in some idempotent and harmonic convex structure

Briec

Yeşilce

2022

Journal of Mathematical Analysis and Applications

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Some general principles in tropical convexities

Abstract: Abstract.We present what the title says with an emphasis on separation and topological properties as they relate to some of the fundamental principles of nonlinear analysis.

Cited by 2 publications

References 13 publications

Tropical convexity in Riesz spaces

Tropical convexity in Riesz spaces

Ky-Fan inequality, Nash equilibria in some idempotent and harmonic convex structure

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