The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications

• Autorzy: George Isac , George Xian-Zhi Yuan
• Języki publikacji: EN

Abstrakty

EN

In this paper, we first establish the dual form of Knaster- Kuratowski-Mazurkiewicz principle which is a hyperconvex version of corresponding result due to Shih. Then Ky Fan type matching theorems for finitely closed and open covers are given. As applications, we establish some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horvath and Lassonde. Then Ky Fan type best approximation theorem and Schauder-Tychonoff fixed point theorem for set-valued mappings (i.e., Fan-Glicksberg fixed point theorem) in hyperconvex spaces are also developed, and finally one unified form of Browder-Fan fixed point theorem for set-valued mappings in hyperconvex spaces is given. These results include corresponding results in the literature due to Khamsi, Kirk and Shin, Kirk et al. as special cases.

Słowa kluczowe

EN

hyperconvex space; admissible set; generalised metric KKM mapping; dual form of KKM principle; Ky Fan matching theorem; Browder-Fan fixed point; Schauder-Tychonoff fixed point; Fan-Glicksberg fixed point and best approximation

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 47H04: Set-valued operators
• 54C60: Set-valued maps
• 49J35: Minimax problems
• 52A99: None of the above, but in this section

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1999
• Tom: 19
• Numer: 1-2
• Strony: 17-33

Daty

wydano

1999

otrzymano

1999-02-05

Twórcy

autor

George Isac

• Department of Mathematics and Computer Sciences, Royal Military College of Canada, Kingston, Ont. Canada K7K 5L0

autor

George Xian-Zhi Yuan

• Department of Mathematics, The University of Queensland, Brisbane, Australia 4072

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