Topics in Nonlinear Analysis and Applications

by Hyers, Donald H.; Isac, George; Rassias, Themistocles M.

• ISBN13: 9789810225346
• ISBN10: 9810225342
• Format: Hardcover
• Copyright: 1996-09-01
• Publisher: World Scientific Pub Co Inc

Table of Contents

Preface	ix
Cones and Complementarity Problems
Introduction	1	(1)
Convex Cones	2	(25)
Normal cones	4	(4)
Regular and completely regular cones	8	(2)
Well based cones	10	(6)
Isotone projection cones	16	(7)
Galerkin cones	23	(4)
Complementarity Problems	27	(20)
The explicit complementarity problem	30	(9)
The implicit complementarity problem	39	(3)
The generalized order complementarity problem	42	(5)
Existence Theorems	47	(85)
Galerkin cones and the generalized Karamardian condition	47	(7)
Galerkin cones and conically coercive functions	54	(5)
Variational inequalities and explicit complementarity problems	59	(10)
Isotone projection cones and complementarity problems	69	(12)
Comment	81	(1)
Complementarity problems and condition (S)1+	82	(13)
S-variational inequalities and the implicit complementarity problem	95	(9)
Heterotonic operators and the generalized order complementarity problem	104	(13)
Topological degree and complementarity	117	(15)
Some Special Problems In Complementarity Theory	132	(8)
Boundedness of the solution-set	132	(3)
Solution which is the least element of the feasible set	135	(4)
The cardinality of the solution-set	139	(1)
Nonexistence of solution	139	(1)
Sensitivity analysis	139	(1)
Nonlinear complementarity and quasi-equilibria	139	(1)
Complementarity And Fixed Points	140	(8)
References	148	(19)
Metrics on Convex Cones
Introduction	167	(3)
Hilbert's Projective Metric	170	(38)
Thompson's Metric	208	(12)
Working With Two Cones	220	(8)
Monotone Semigroups And Metrics On Cones	228	(5)
References	233	(8)
Zero-Epi Mappings
Introduction	241	(2)
Zero-EPI Mappings On Bounded Sets	243	(12)
Zero-EPI Mappings On The Whole Space	255	(16)
Zero-EPI Mappings On Cones	271	(13)
Zero-EPI Families Of Mappings And Optimization	284	(20)
Zero-EPI Mappings And Complementarity Problems	304	(11)
Zero-EPI Mappings And k-Set Contraction	315	(3)
References	318	(7)
Variational Principles
Introduction	325	(3)
Preliminaries	328	(15)
Critical Points For Dynamical Systems	343	(12)
Variants Of Ekeland's Variational Principle	355	(10)
The Drop Theorem	365	(14)
Strong Forms And Generalizations Of Ekeland's Principle	379	(47)
Equivalencies	426	(7)
Ekeland's Variational Principle For Vector Valued Functions	433	(11)
Applications	444	(95)
Existence of solutions for minimizing problems	444	(8)
Coercivity condition	452	(2)
A global variational principle on cones	454	(9)
Density result	463	(1)
Mountain pass lemma	464	(13)
The Bishop-Phelps theorem	477	(3)
Clarke's fixed point theorem	480	(4)
Borwein's &epsis;-principle	484	(4)
Φ-accretive operators and surjectivity	488	(6)
Zabreiko-Krasnoselskii's theorem	494	(3)
The drop property and the geometry of Banach spaces	497	(22)
The drop property for arbitrary sets	519	(20)
References	539	(16)
Maximal Element Principles
Introduction	555	(1)
Preliminaries	556	(6)
Variation On Zorn's Lemma	562	(14)
Applications	567	(8)
Comments	575	(1)
New Maximal Element Principles	576	(65)
Applications	608	(1)
A fixed point theorem for ordered sets	608	(1)
Maximality and solvability	609	(9)
Variable drops and general solvability	618	(6)
A drop theorem	624	(2)
Lipschitzianess tests	626	(7)
Maximal element principles and general Newton-Kantorovich processes	633	(7)
Comments	640	(1)
Pareto Efficiency	641	(31)
References	672	(13)
Symbol Index	685	(6)
Subject Index	691