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Topological methods for set-valued nonlinear analysis /
This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical eco...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ :
World Scientific,
©2008.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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. 2.3. Further generalization of Banach contraction mapping principle. 2.4. Changing norm. 2.5. The contraction mapping principle applied to the Cauchy-Kowalevsky theorem. 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. 2.7. Set-valued contractions. 2.8. Iterated Function Systems (IFS) and attractor. 2.9. Large contractions. 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. 3.4. 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 (2[symbol], [symbol]). 3.8. The iterated function systems on (C(X), [symbol]). 3.9. The iterated function system on (K(X), [symbol]). 3.10. Continuity of maps on countably compact and sequential spaces. 3.11. Solutions of impulsive differential equations
- 4. Topological fixed point theorems. 4.1. Brouwer fixed point theorem. 4.2. Fixed point theorems and KKM theorems. 4.3. Applications on Minimax principles. 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. 4.9. Fixed point of [symbol]-condensing mapping, maximal elements and equilibria. 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. 5.2. Variational inequalities for setvalued mappings. 5.3. Variational inequalities and applications. 5.4. Duality in variational inequalities. 5.5. A variational inequality in non-compact sets with some applications. 5.6. Browder-Hartman-Stampacchia variational inequalities for set-valued monotone operators. 5.7. Some generalized variational inequalities with their applications. 5.8. Some results of Tarafdar and Yuan on generalized variational inequalities in locally convex topological vector spaces. 5.9. Generalized variational inequalities for quasi-monotone and quasi- semi-monotone operators. 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. 5.11. Generalized variational-like inequalities for pseudo-monotone type I operators. 5.12. Generalized quasi-variational inequalities. 5.13. Generalized quasi-variational inequalities for lower and upper hemi-continuous operators on non-compact sets. 5.14. Generalized quasi-variational inequalities for upper semi-continuous operators on non-compact sets. 5.15. 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. 5.17. Equilibria of non-compact generalized games with L*. 5.18. Equilibria of non-compact generalized 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
- 7. Degree theories for set-valued mappings. 7.1. Degree theory for set-valued ultimately compact vector fields. 7.2. Coincidence degree for non-linear single-valued perturbations of linear Fredholm mappings. 7.3. On the existence of solutions of the equation Lx [symbol] Nx and a coincidence degree theory. 7.4. Coincidence degree for multi-valued mappings with non-negative index. 7.5. Applications of equivalence theorems with single-valued mappings: an approach to non-linear 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. 7.8. Tarafdar and Thompson's results on the solvability of non-linear and non-compact operator equations
- 8. Nonexpansive types of mappings and fixed point pheorems in locally convex topological vector spaces. 8.1. Nonexpansive types of mappings in locally convex topological vector spaces. 8.2. Set-valued mappings of nonexpansive type. 8.3. Fixed point theorems for condensing set-valued mappings on locally convex topological vector spaces.