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Tables of Contents for Minimax Theory and Applications
Chapter/Section Title
Page #
Page Count
Preface
xi
 
Nonlinear Two Functions Minimax Theorems
1
20
Cao-Zong Cheng
Bor-Luh Lin
1. Introduction
1
4
2. Nonlinear Minimax Theorems
5
5
3. Two Functions Minimax Theorems of Type A/Type B
10
8
4. Two Functions Minimax Theorems of Mixed Type
18
1
References
19
2
Weakly Upward-Downward Minimax Theorem
21
8
Cao-Zong Cheng
Bor-Luh Lin
Feng-Shuo Yu
References
28
1
A Two-Function Minimax Theorem
29
6
Antonia Chinni
1. Introduction
29
1
2. The Main Result
30
1
3. Remarks and Examples Related to Theorem 2.2
31
2
References
33
2
Generalized Fixed-Points and Systems of Minimax Inequalities
35
6
Paul Deguire
1. Introduction
35
1
2. Applications
36
4
References
40
1
A Minimax Inequality for Marginally Semicontinuous Functions
41
12
Gabriele H. Greco
Maria Pia Moschen
References
50
3
On Variational Minimax Problems under Relaxed Coercivity Assumptions
53
18
Joachim Gwinner
1. Introduction
53
2
2. Some Preliminary Remarks
55
2
3. A Unilateral Boundary Value Problem and its Variational Mimimax Formulation
57
3
4. The Semicoercive Case
60
4
5. Lagrangian Minimax Problems
64
5
References
69
2
A Topological Investigation of the Finite Intersection Property
71
20
Charles D. Horvath
1. Introduction
71
3
2. The Finite Intersection Property
74
7
3. Topological Spaces with a Convexity Structure
81
7
4. Conclusion
88
1
References
89
2
Minimax Results and Randomization for Certain Stochastic Games
91
14
Albrecht Irle
1. Introduction
91
2
2. Randomization of Stopping Times
93
2
3. Compact Embedding and Equivalence of Randomization
95
3
4. Minimax Results in Discrete Time
98
1
5. A Minimax Result in Continuous Time
99
4
References
103
2
Intersection Theorems, Minimax Theorems and Abstract Connectedness
105
16
Jurgen Kindler
1. Introduction
105
2
2. Abstract Continuity
107
1
3. Abstract Connectedness
108
2
4. Intersection Theorems
110
3
5. Minimax Theorems
113
7
References
120
1
K-K-M-S Type Theorems in Infinite Dimensional Spaces
121
14
Hidetoshi Komiya
1. Introduction
121
1
2. Selection of Base Spaces and Preliminaries
122
1
3. Balanced Families
123
4
4. K-K-M-S Type Theorems in Infinite Dimensional Spaces
127
3
5. Application to Game Theory
130
2
6. Extensions of K-K-M-S Theorem
132
2
References
134
1
Hahn-Banach Theorems for Convex Functions
135
12
Marc Lassonde
1. Separation of Convex Functions
137
3
2. Continuity of Convex Functions
140
4
References
144
3
Two Functions Generalization of Horvath's Minimax Theorem
147
10
Bor-Luh Lin
Feng-Shuo Yu
References
156
1
Some Remarks on a Minimax Formulation of a Variational Inequality
157
10
Giandomenico Mastroeni
1. Saddle Point Conditions and Variational Inequalities
157
2
2. Applications to the Classical Variational Inequality
159
2
3. Connections with Complementarity Problems
161
1
4. Vector Variational Inequalities
162
2
5. Further Developments
164
2
References
166
1
Network Analysis
167
24
Michael M. Neumann
Maria Victoria Velasco
1. Introduction
167
1
2. From Finite to Infinite Networks
167
3
3. Tools from Functional Analysis
170
3
4. Existence of Flows
173
5
5. Existence of Potentials
178
2
6. Symmetric, Antisymmetric and Net Flows
180
5
7. Marginal Problems
185
1
8. Concluding Remarks
186
2
References
188
3
On a Topological Minimax Theorem and its Applications
191
26
Biagio Ricceri
1. Introduction
191
2
2. Preliminaries
193
3
3. Proof of Theorem 1.1
196
2
4. An Application of Theorem 1.1 to the Problem inf(X) f = inf(d)(X) f
198
5
5. A Variational Property of Integral-Functionals
203
13
References
216
1
Three Lectures on Minimax and Monotonicity
217
24
Stephen Simons
0. Introduction
217
2
1. Multifunctions and Monotonicity
219
2
2. A Convexification of E x E(*) and the Three Affine Maps
221
1
3. Monotone Subsets and their "Pictures"
222
2
4. For Reflexive Spaces Only
224
3
5. The Convex Function Determined by a Multifunction
227
1
6. Surrounding Sets and the Dom-Dom Lemma
228
6
7. The "Dom-Dom Constraint Qualification"
234
2
8. A "Sum Theorem" for Reflexive Spaces
236
3
References
239
2
Fan's Existence Theorem for Inequalities Concerning Convex Functions and its Applications
241
20
Wataru Takahashi
1. Introduction
241
1
2. Generalization of Fan's System Theorem
242
6
3. Basic Results in Functional Analysis
248
4
4. Applications
252
7
References
259
2
An Algorithim for the Multi-Access Channel Problem
261
10
Peng-Jung Wan
Ding-Zu Du
Panos M. Pardalos
1. Introduction
262
1
2. The Algorithm
262
3
3. Analysis
265
4
4. Conclusion
269
1
References
269
2
Author Index
271