M-convexity, extension and equilibrium existence theorems in G-convex spaces.
Date
1998
Authors
Afghani, Obaidah Mohammad.
Journal Title
Journal ISSN
Volume Title
Publisher
Dalhousie University
Abstract
Description
This thesis is devoted to the study of G-convex spaces.
In Chapter 1, we introduce the new concepts of M-convex spaces and M-convexity. We present a KKM-type theorem, and two fixed point theorems which illustrate the significance of these concepts. We also define a G-convex structure on the product of a family of G-convex spaces.
In Chapter 2, we prove that any complete metric space with a continuous midpoint function is a G-convex space.
In Chapter 3, we prove several Dugundji-type extension theorems in G-convex spaces. Both cases of single and set-valued maps are considered. Important applications to the theory of games are obtained from these extension theorems.
In Chapter 4, we define M-convexity and M-concavity for real functions on an M-convex space. A continuous dual is also defined and we give solutions for some variational inequalities.
In Chapter 5, we define classes of GLS and GLS -majorized correspondences. We obtain some maximal element theorems for these correspondences and apply them to generalized games and minimax inequalities.
Thesis (Ph.D.)--Dalhousie University (Canada), 1998.
In Chapter 1, we introduce the new concepts of M-convex spaces and M-convexity. We present a KKM-type theorem, and two fixed point theorems which illustrate the significance of these concepts. We also define a G-convex structure on the product of a family of G-convex spaces.
In Chapter 2, we prove that any complete metric space with a continuous midpoint function is a G-convex space.
In Chapter 3, we prove several Dugundji-type extension theorems in G-convex spaces. Both cases of single and set-valued maps are considered. Important applications to the theory of games are obtained from these extension theorems.
In Chapter 4, we define M-convexity and M-concavity for real functions on an M-convex space. A continuous dual is also defined and we give solutions for some variational inequalities.
In Chapter 5, we define classes of GLS and GLS -majorized correspondences. We obtain some maximal element theorems for these correspondences and apply them to generalized games and minimax inequalities.
Thesis (Ph.D.)--Dalhousie University (Canada), 1998.
Keywords
Mathematics.