Fixed point and maximal element theorems with applications to abstract economies and minimax inequalities

Lai Jiu Lin; Zenn Tsuen Yu; Qamrul Hasan Ansari; Li Ping Lai

doi:10.1016/S0022-247X(03)00385-8

Fixed point and maximal element theorems with applications to abstract economies and minimax inequalities

Lai Jiu Lin^*
, Zenn Tsuen Yu
, Qamrul Hasan Ansari
, Li Ping Lai

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

47 Scopus citations

Abstract

In this paper, we establish some fixed point theorems for a family of multivalued maps under mild conditions. By using our fixed point theorems, we derive some maximal element theorems for a particular family of multivalued maps, namely the Φ-condensing multivalued maps. As applications of our results, we prove some general equilibrium existence theorems in the generalized abstract economies with preference correspondences. Further applications of our results are also given to minimax inequalities for a family of functions.

Original language	English
Pages (from-to)	656-671
Number of pages	16
Journal	Journal of Mathematical Analysis and Applications
Volume	284
Issue number	2
DOIs	https://doi.org/10.1016/S0022-247X(03)00385-8
State	Published - 15 Aug 2003
Externally published	Yes

Keywords

Fixed point theorems
Generalized abstract economies
Maximal element theorems
Minimax inequalities
Transfer compactly open valued maps
Φ-condensing multivalued maps

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/S0022-247X(03)00385-8

Cite this

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title = "Fixed point and maximal element theorems with applications to abstract economies and minimax inequalities",

abstract = "In this paper, we establish some fixed point theorems for a family of multivalued maps under mild conditions. By using our fixed point theorems, we derive some maximal element theorems for a particular family of multivalued maps, namely the Φ-condensing multivalued maps. As applications of our results, we prove some general equilibrium existence theorems in the generalized abstract economies with preference correspondences. Further applications of our results are also given to minimax inequalities for a family of functions.",

keywords = "Fixed point theorems, Generalized abstract economies, Maximal element theorems, Minimax inequalities, Transfer compactly open valued maps, Φ-condensing multivalued maps",

author = "Lin, \{Lai Jiu\} and Yu, \{Zenn Tsuen\} and Ansari, \{Qamrul Hasan\} and Lai, \{Li Ping\}",

year = "2003",

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doi = "10.1016/S0022-247X(03)00385-8",

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AU - Lin, Lai Jiu

AU - Yu, Zenn Tsuen

AU - Ansari, Qamrul Hasan

AU - Lai, Li Ping

PY - 2003/8/15

Y1 - 2003/8/15

N2 - In this paper, we establish some fixed point theorems for a family of multivalued maps under mild conditions. By using our fixed point theorems, we derive some maximal element theorems for a particular family of multivalued maps, namely the Φ-condensing multivalued maps. As applications of our results, we prove some general equilibrium existence theorems in the generalized abstract economies with preference correspondences. Further applications of our results are also given to minimax inequalities for a family of functions.

AB - In this paper, we establish some fixed point theorems for a family of multivalued maps under mild conditions. By using our fixed point theorems, we derive some maximal element theorems for a particular family of multivalued maps, namely the Φ-condensing multivalued maps. As applications of our results, we prove some general equilibrium existence theorems in the generalized abstract economies with preference correspondences. Further applications of our results are also given to minimax inequalities for a family of functions.

KW - Fixed point theorems

KW - Generalized abstract economies

KW - Maximal element theorems

KW - Minimax inequalities

KW - Transfer compactly open valued maps

KW - Φ-condensing multivalued maps

UR - https://www.scopus.com/pages/publications/0042353638

U2 - 10.1016/S0022-247X(03)00385-8

DO - 10.1016/S0022-247X(03)00385-8

M3 - Article

AN - SCOPUS:0042353638

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VL - 284

SP - 656

EP - 671

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Fixed point and maximal element theorems with applications to abstract economies and minimax inequalities

Abstract

Keywords

ASJC Scopus subject areas

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