Contents 1. Introduction 2. The classical model 3. Existence of equilibrium 3.1 Equilibrium and quasi-equilibrium of abstract economies 3.2 Application to quasi-equilibrium existence for private ownership economies 3.3 From quasi-equilibrium to equilibrium 4. Optimality properties of equilibrium 4.1 Optimality, core and limit-core concepts 4.2 Non-emptiness results 4.3 Price-decentralization re...

1. Introduction: In the research area of one dimensional stochastic processes, Markov chains acquire special importance due to large number of applications. One of the simplest possible continuous time Markov chains, namely birth-and-death process arises naturally in many queueing models. Such a Markov chain has an efficient recursive solution for the equilibrium probabilities. Specifically the...

This paper is devoted to the characterizations of the boundedness and nonemptiness of solution sets for set-valued vector equilibrium problems in reflexive Banach spaces, when both themapping and the constraint set are perturbed by different parameters. By using the properties of recession cones, several equivalent characterizations are given for the set-valued vector equilibrium problems to ha...

1. Incompleteness of weak duals of reasonable spaces 2. Appendix: locally-convex limits and colimits 3. Appendix: ubiquity of quasi-completeness The point here is to prove that the weak duals of reasonable topological vector spaces, such as infinite-dimensional Hilbert, Banach, or Fréchet spaces, are not complete. That is, in these weak duals there are Cauchy nets which do not converge. Happily...

The purpose of this paper is to introduce a new generalized system of nonlinear quasi-mixed equilibrium problems and find the common solutions of this problem and a fixed point problem. The results obtained in this paper may be viewed as an extension, refinement and improvement of the previously known results in [2-4] and others. Mathematics Subject Classification: 47H09, 47J25