<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Paraconvex multimaps are revisited in normed vector space setting. A parallel is provided with the studies conducted for real valued paraconvex functions on generalized convexities and monotonicities. Several characterizations are then obtained. The links with some generalized convexities for multimaps are examined and a first classification is achieved. In addition, two representation results for 2-paraconvex multimaps are given.</p>
</abstract>

Paraconvex multimaps are revisited in normed vector space setting. A parallel is provided with the studies conducted for real valued paraconvex functions on generalized convexities and monotonicities. Several characterizations are then obtained. The links with some generalized convexities for multimaps are examined and a first classification is achieved. In addition, two representation results for 2-paraconvex multimaps are given.

Characterizations and Classification of Paraconvex Multimaps

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Characterizations and Classification of Paraconvex Multimaps"}

Paraconvex multimaps are revisited in normed vector space setting. A parallel is provided with the studies conducted for real valued paraconvex functions on...

Characterizations and Classification of Paraconvex Multimaps

Publié en ligne: 22 mars 2023

Pages: 303 - 325

Reçu: 01 janv. 2022

Accepté: 01 avr. 2022

DOI: https://doi.org/10.2478/candc-2022-0019

Mots clés
support function, paraconvex multimap, Lipschitz property, generalized convexities, submonotonicity

© 2022 Hocine Mokhtar-Kharroubi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Characterizations and Classification of Paraconvex Multimaps

Publié en ligne: 22 mars 2023

Pages: 303 - 325

Reçu: 01 janv. 2022

Accepté: 01 avr. 2022

DOI: https://doi.org/10.2478/candc-2022-0019

Mots cléssupport function, paraconvex multimap, Lipschitz property, generalized convexities, submonotonicity

© 2022 Hocine Mokhtar-Kharroubi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
support function, paraconvex multimap, Lipschitz property, generalized convexities, submonotonicity