{"title":"集值正交性和逼近性","authors":"A. Barbagallo, Octavian-Emil Ernst, Michel Théra","doi":"10.1478/AAPP.98S2A2","DOIUrl":null,"url":null,"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.","PeriodicalId":43431,"journal":{"name":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2020-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SET-VALUED ORTHOGONALITY AND NEARNESS\",\"authors\":\"A. Barbagallo, Octavian-Emil Ernst, Michel Théra\",\"doi\":\"10.1478/AAPP.98S2A2\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":43431,\"journal\":{\"name\":\"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-02-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1478/AAPP.98S2A2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1478/AAPP.98S2A2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
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.
期刊介绍：
This journal is of a multi- and inter-disciplinary nature and covers a broad range of fields including mathematics, computer science, physics, chemistry, biology, earth sciences, and their intersection. History of science is also included within the topics addressed by the journal. The transactions of the Pelorian Academy started out as periodic news sheets containing the notes presented by the members of the Divisions into which the Academy has been and still is organized, according to subject areas. The publication of these notes for the Division (“Classe”) of Mathematical, Physical and Natural Sciences is the responsibility of the Editorial Committee, which is composed of the Director of the division with the role of Chairman, the Vice-Director, the Secretary and two or more other members. Besides original research articles, the journal also accepts texts from conferences and invited talks held in the Academy. These contributions are published in a different section of the journal. In addition to the regular issues, single monographic supplements are occasionally published which assemble reports and communications presented at congresses, symposia, seminars, study meetings and other scientific events organized by the Academy or under its patronage. Since 2004 these transactions have been published online in the form of an open access electronic journal.
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