<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

Published Online: Mar 22, 2023

Page range: 303 - 325

Received: Jan 01, 2022

Accepted: Apr 01, 2022

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

Keywords
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

Published Online: Mar 22, 2023

Page range: 303 - 325

Received: Jan 01, 2022

Accepted: Apr 01, 2022

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

Keywordssupport 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.

Keywords
support function, paraconvex multimap, Lipschitz property, generalized convexities, submonotonicity