Contents -- Preface -- 1. Introduction -- 2. Contraction Mappings -- 2.1 Contraction Mapping Principle in Uniform Topological Spaces and Applications -- 2.2 Banach Contraction Mapping Principle in Uniform Spaces -- 2.2.1 Successive Approximation -- 2.3 Further Generalization of Banach Contraction Mapping Principle -- 2.3.1 Fixed Point Theorems for Some Extension of Contraction Mappings on Uniform Spaces -- 2.3.2 An Interplay Between the Order and Pseudometric Partial Ordering in Complete Uniform Topological Space -- 2.4 Changing Norm -- 2.4.1 Changing the Norm -- 2.4.2 On the Approximate Iteration -- 2.5 The Contraction Mapping Principle Applied to the Cauchy- Kowalevsky Theorem -- 2.5.1 Geometric Preliminaries -- 2.5.2 The Linear Problem -- 2.5.3 The Quasilinear Problem -- 2.6 An Implicit Function Theorem for a Set of Mappings and Its Application to Nonlinear Hyperbolic Boundary Value Problem as Application of Contraction Mapping Principle -- 2.6.1 An Implicit Function Theorem for a Set of Mappings -- 2.6.2 Notations and Preliminaries -- 2.6.3 Results of Smiley on Linear Problem -- 2.6.4 Alternative Problem and Approximate Equations -- 2.6.5 Application to Nonlinear Wave Equations - A Theorem of Paul Rabinowitz -- 2.7 Set-Valued Contractions -- 2.7.1 End Points -- 2.8 Iterated Function Systems (IFS) and Attractor -- 2.8.1 Applications -- 2.9 Large Contractions -- 2.9.1 Large Contractions -- 2.9.2 The Transformation -- 2.9.3 An Existence Theorem -- 2.10 Random Fixed Point and Set-Valued Random Contraction -- 3. Some Fixed Point Theorems in Partially Ordered Sets -- 3.1 Fixed Point Theorems and Applications to Economics -- 3.2 Fixed Point Theorem on Partially Ordered Sets -- 3.3 Applications to Games and Economics -- 3.3.1 Game -- 3.3.2 Economy -- 3.3.3 Pareto Optimum.

3.3.4 The Contraction Mapping Principle in Uniform Space via Kleene's Fixed Point Theorem -- 3.3.5 Applications on Double Ranked Sequence -- 3.4 Lattice Theoretical Fixed Point Theorems of Tarski -- 3.5 Applications of Lattice Fixed Point Theorem of Tarski to Integral Equations -- 3.6 The Tarski-Kantorovitch Principle -- 3.7 The Iterated Function Systems on (2X -- ) -- 3.8 The Iterated Function Systems on (C(X) -- ) -- 3.9 The Iterated Function System on (K(X) -- ) -- 3.10 Continuity of Maps on Countably Compact and Sequential Spaces -- 3.11 Solutions of Impulsive Differential Equations -- 3.11.1 A Comparison Result . -- 3.11.2 Periodic Solutions -- 4. Topological Fixed Point Theorems -- 4.1 Brouwer Fixed Point Theorem -- 4.1.1 Schauder Projection -- 4.1.2 Fixed Point Theorems of Set Valued Mappings with Applications in Abstract Economy -- 4.1.3 Applications -- 4.1.4 Equilibrium Point of Abstract Economy -- 4.2 Fixed Point Theorems and KKM Theorems -- 4.2.1 Duality in Fixed Point Theory of Set Valued Mappings -- 4.3 Applications on Minimax Principles -- 4.3.1 Applications on Sets with Convex Sections -- 4.4 More on Sets with Convex Sections -- 4.5 More on the Extension of KKM Theorem and Ky Fan's Minimax Principle -- 4.6 A Fixed Point Theorem Equivalent to the Fan-Knaster- Kuratowski-Mazurkiewicz Theorem -- 4.7 More on Fixed Point Theorems -- 4.8 Applications of Fixed Point Theorems to Equilibrium Analysis in Mathematical Economics and Game Theory -- 4.8.1 Fixed Point and Equilibrium Point -- 4.8.2 Existence of Maximal Elements -- 4.8.3 Equilibrium Existence Theorems -- 4.9 Fixed Point of -Condensing Mapping, Maximal Elements and Equilibria -- 4.9.1 Equilibrium on Paracompact Spaces -- 4.9.2 Equilibria of Generalized Games -- 4.9.3 Applications -- 4.10 Coincidence Points and Related Results, an Analysis on H-Spaces.

4.11 Applications to Mathematical Economics: An Analogue of Debreu's Social Equilibrium Existence Theorem -- 5. Variational and Quasivariational Inequalities in Topological Vector Spaces and Generalized Games -- 5.1 Simultaneous Variational Inequalities -- 5.1.1 Variational Inequalities for Single Valued Functions -- 5.1.2 Solutions of Simultaneous Nonlinear Variational Inequalities -- 5.1.3 Application to Nonlinear Boundary Value Problem for Quasilinear Operator of Order 2m in Generalized Divergence Form -- 5.1.4 Minimization Problems and Related Results -- 5.1.5 Extension of a Karamardian Theorem -- 5.2 Variational Inequalities for Setvalued Mappings -- 5.2.1 Simultaneous Variational Inequalities -- 5.2.2 Implicit Variational Inequalities - The Monotone Case -- 5.2.3 Implicit Variational Inequalities - The USC Case -- 5.3 Variational Inequalities and Applications -- 5.3.1 Application to Minimization Problems -- 5.4 Duality in Variational Inequalities -- 5.4.1 Some Auxiliary Results -- 5.5 A Variational Inequality in Non-Compact Sets with Some Applications -- 5.6 Browder-Hartman-Stampacchia Variational Inequalities for Set-Valued Monotone Operators -- 5.6.1 A Minimax Inequality -- 5.6.2 An Existence Theorem of Variational Inequalities -- 5.7 Some Generalized Variational Inequalities with Their Applications -- 5.7.1 Some Generalized Variational Inequalities -- 5.7.2 Applications to Minimization Problems -- 5.8 Some Results of Tarafdar and Yuan on Generalized Variational Inequalities in Locally Convex Topological Vector Spaces -- 5.8.1 Some Generalized Variational Inequalities -- 5.9 Generalized Variational Inequalities for Quasi-Monotone and Quasi- Semi-Monotone Operators -- 5.9.1 Generalization of Ky Fan's Minimax Inequality -- 5.9.2 Generalized Variational Inequalities -- 5.9.3 Fixed Point Theorems.

5.10 Generalization of Ky Fan's Minimax Inequality with Applications to Generalized Variational Inequalities for Pseudo-Monotone Type I Operators and Fixed Point Theorems -- 5.10.1 Generalization of Ky Fan's Minimax Inequality -- 5.10.2 Generalized Variational Inequalities -- 5.10.3 Applications to Fixed Point Theorems -- 5.11 Generalized Variational-Like Inequalities for Pseudo-Monotone Type I Operators -- 5.11.1 Existence Theorems for GV LI(T -- -- h -- X -- F) -- 5.12 Generalized Quasi-Variational Inequalities -- 5.12.1 Generalized Quasi-Variational Inequalities for Monotone and Lower Semi-Continuous Mappings -- 5.12.2 Generalized Quasi-Variational Inequalities for Upper Semi- Continuous Mappings Without Monotonicity -- 5.13 Generalized Quasi-Variational Inequalities for Lower and Upper Hemi-Continuous Operators on Non-Compact Sets -- 5.13.1 Generalized Quasi-Variational Inequalities for Lower Hemi- Continuous Operators -- 5.13.2 Generalized Quasi-Variational Inequalities for Upper Hemi- Continuous Operators -- 5.14 Generalized Quasi-Variational Inequalities for Upper Semi- Continuous Operators on Non-Compact Sets -- 5.14.1 Non-Compact Generalized Quasi-Variational Inequalities -- 5.15 Generalized Quasi-Variational Inequalities for Pseudo-Monotone Set-Valued Mappings -- 5.15.1 Generalized Quasi-Variational Inequalities for Strong Pseudo- Monotone Operators -- 5.15.2 Generalized Quasi-Variational Inequalities for Pseudo- Monotone Set-Valued Mappings -- 5.16 Non-Linear Variational Inequalities and the Existence of Equilibrium in Economics with a Riesz Space of Commodities -- 5.16.1 Existence of Equilibrium Lemma -- 5.17 Equilibria of Non-compact Generalized Games with L Majorized Preference Correspondences -- 5.17.1 Existence of Maximal Elements -- 5.17.2 Existence of Equilibrium for Non-Compact Abstract Economies.

5.18 Equilibria of Non-Compact Generalized Games -- 5.18.1 Equilibria of Generalized Games -- 5.18.2 Tarafdar and Yuan's Application on Existence Theorem of Equilibria for Constrained Games -- 6. Best Approximation and Fixed Point Theorems for Set-Valued Mappings in Topological Vector Spaces -- 6.1 Single-Valued Case -- 6.2 Set-Valued Case -- 6.2.1 Some Lemmas and Relevant Results -- 7. Degree Theories for Set-Valued Mappings -- 7.1 Degree Theory for Set-Valued Ultimately Compact Vector Fields -- 7.1.1 Properties of the Degree of Ultimately Compact Vector Fields -- 7.1.2 k- -Contractive Set Valued Mappings -- 7.2 Coincidence Degree for Non-Linear Single-Valued Perturbations of Linear Fredholm Mappings -- 7.2.1 An Equivalence Theorem -- 7.2.2 Definition of Coincidence Degree -- 7.2.3 Properties of the Coincidence Degree -- 7.3 On the Existence of Solutions of the Equation Lx 2 Nx and a Coincidence Degree Theory -- 7.3.1 Coincidence Degree for Set-Valued k -- 7.4 Coincidence Degree for Multi-Valued Mappings with Non-Negative Index -- 7.4.1 Basic Assumptions and Main Results in Akashi (1988) -- 7.4.2 Akashi's Basic Properties of Coincidence Degree -- 7.4.3 Application to Multitivalued Boundary Value Problem for Elliptic Partial Differential Equation -- 7.5 Applications of Equivalence Theorems with Single-Valued Mappings: An Approach to Non-Linear Elliptic Boundary Value Problems -- 7.5.1 Tarafdar's Application to Elliptic Boundary Value Problems -- 7.6 Further Results in Coincidence Degree Theory -- 7.7 Tarafdar and Thompson's Theory of Bifurcation for the Solutions of Equations Involving Set-Valued Mapping -- 7.7.1 Characteristic Value and Multiplicity -- 7.7.2 Tarafdar and Thompson's Results on the Theory of Bifurcation -- 7.7.3 Tarafdar and Thompson's Application on the Theory of Bifurcation.

7.8 Tarafdar and Thompson's Results on the Solvability of Non-Linear and Non-Compact Operator Equations.