Set-valued orthogonality and nearness

Authors

  • Annamaria Barbagallo University of Naples Federico II
  • Octavian E. Ernst Aix-Marseille Université
  • Michel Théra Université de Limoges and Federation University Australia https://orcid.org/0000-0001-9022-6406

DOI:

https://doi.org/10.1478/AAPP.98S2A2

Keywords:

Campanato nearness, Birkoff-James orthogonality, set-valued mappings

Abstract

The theory of set-valued mappings has grown with the development of modern variational analysis. It is a key in convex and non-smooth analysis, in game theory, in mathematical economics and in control theory. The concepts of nearness and orthogonality have been known for functions since the pioneering works of Campanato, Birkhoff and James. In a recent paper Barbagallo et al. [J. Math. Anal. Appl., 484 (1), (2020)] a connection between these two concepts has been made. This note is mainly devoted to introduce nearness and orthogonality between set-valued mappings with the goal to study the solvability of generalized equations involving set-valued mappings.

Author Biographies

  • Annamaria Barbagallo, University of Naples Federico II
    Department of Mathematics and Applications R. Caccioppoli
  • Octavian E. Ernst, Aix-Marseille Université
    Institut de Mathématiques de Marseille
  • Michel Théra, Université de Limoges and Federation University Australia
    Professor Emeritus (classe exceptionnelle), University of Limoges, and Adjunct Professor, Federation University Australia

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Published

2020-12-13

Issue

Vol 98, SUPPL NO 2 (2020): VA.PDE.ME.19

Section

Variational Analysis, PDEs and Mathematical Economics (Conference Proceedings)

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