Characterizations and Classification of Paraconvex Multimaps

Hocine Mokhtar-Kharroubi

doi:10.2478/candc-2022-0019

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Characterizations and Classification of Paraconvex Multimaps

Control and Cybernetics

Volume 51 (2022): Issue 3 (September 2022)

By: Hocine Mokhtar-Kharroubi

Open Access

|Mar 2023

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.

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Articles in this issue

DOI: https://doi.org/10.2478/candc-2022-0019 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569

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Language: English

Page range: 303 - 325

Submitted on: Jan 1, 2022

Accepted on: Apr 1, 2022

Published on: Mar 22, 2023

Published by: Systems Research Institute Polish Academy of Sciences

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

support function,

paraconvex multimap,

Lipschitz property,

generalized convexities,

submonotonicity

Related subjects:

Computer sciences,

Computer sciences, other,

Engineering,

Electrical engineering,

Fundamentals of electrical engineering,

Mechanical engineering,

Fundamentals of mechanical engineering,

Mathematics,

General mathematics

© 2023 Hocine Mokhtar-Kharroubi, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 51 (2022): Issue 3 (September 2022)