6,817 research outputs found
Equilibrium problems on Riemannian manifolds with applications
We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable variational inequality problem on Riemannian manifolds, and is completely different from previous ones on this topic in the literature. As applications, the corresponding results for the mixed variational inequality and the Nash equilibrium are obtained. Moreover, we formulate and analyze the convergence of the proximal point algorithm for the equilibrium problem. In particular, correct proofs are provided for the results claimed in J. Math. Anal. Appl. 388, 61-77, 2012 (i.e., Theorems 3.5 and 4.9 there) regarding the existence of the mixed variational inequality and the domain of the resolvent
for the equilibrium problem on Hadamard manifolds.National Natural Science Foundation of ChinaNatural Science Foundation of Guizhou Province (China)Dirección General de Enseñanza SuperiorJunta de AndalucíaNational Science Council of Taiwa
Existence of Equilibrium in Minimax Inequalities, Saddle, Points, Fixed Points, and Games without Convexity Sets
minimax inequality, saddle points, fixed points, coincidence points, discontinuity, non-quasiconcavity, non-convexity, and non-compactness
New results on systems of generalized vector quasi-equilibrium problems
In this paper, we firstly prove the existence of the equilibrium for the
generalized abstract economy. We apply these results to show the existence of
solutions for systems of vector quasi-equilibrium problems with multivalued
trifunctions. Secondly, we consider the generalized strong vector
quasi-equilibrium problems and study the existence of their solutions in the
case when the correspondences are weakly naturally quasi-concave or weakly
biconvex and also in the case of weak-continuity assumptions. In all
situations, fixed-point theorems are used.Comment: 24 page
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