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

George Isac; George Xian-Zhi Yuan

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1999)

  • Volume: 19, Issue: 1-2, page 17-33
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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George Isac, and George Xian-Zhi Yuan. "The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 19.1-2 (1999): 17-33. <http://eudml.org/doc/275868>.

@article{GeorgeIsac1999,
abstract = {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.},
author = {George Isac, George Xian-Zhi Yuan},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {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; fixed point theorems; intersection theorems; Knaster-Kuratowski-Mazurkiewicz principle; Ky-Fan-type matching theorems; best approximation theorem},
language = {eng},
number = {1-2},
pages = {17-33},
title = {The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications},
url = {http://eudml.org/doc/275868},
volume = {19},
year = {1999},
}

TY - JOUR
AU - George Isac
AU - George Xian-Zhi Yuan
TI - The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1999
VL - 19
IS - 1-2
SP - 17
EP - 33
AB - 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.
LA - eng
KW - 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; fixed point theorems; intersection theorems; Knaster-Kuratowski-Mazurkiewicz principle; Ky-Fan-type matching theorems; best approximation theorem
UR - http://eudml.org/doc/275868
ER -

References

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