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.
Set-valued orthogonality and nearness / Barbagallo, A.; Ernst, O. -E.; Thera, M.. - In: ATTI DELLA ACCADEMIA PELORITANA DEI PERICOLANTI, CLASSE DI SCIENZE FISICHE MATEMATICHE E NATURALI. - ISSN 0365-0359. - 98:(2020). [10.1478/AAPP.98S2A2]
Set-valued orthogonality and nearness
Barbagallo A.
;Thera M.
2020
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
