Author(s): Xian-Zhi Yuan
Journal: Journal of Applied Mathematics and Stochastic Analysis
ISSN 1048-9533
Volume: 7;
Issue: 4;
Start page: 467;
Date: 1994;
Original page
Keywords: Polish space | Suslin space | measurable space | Suslin family | (random) fixed point | (random) maximal element | (random) equilibria | (random) qualitative game | (random) generalized game | (random) variational inequality | (random) quasi-variational inequality | class L | L-majorized | measurable selection theorem | property (K) | random operator.
ABSTRACT
In this paper, existence theorems of random maximal elements, random equilibria for the random one-person game and random generalized game with a countable number of players are given as applications of random fixed point theorems. By employing existence theorems of random generalized games, we deduce the existence of solutions for non-compact random quasi-variational inequalities. These in turn are used to establish several existence theorems of noncompact generalized random quasi-variational inequalities which are either stochastic versions of known deterministic inequalities or refinements of corresponding results known in the literature.
Journal: Journal of Applied Mathematics and Stochastic Analysis
ISSN 1048-9533
Volume: 7;
Issue: 4;
Start page: 467;
Date: 1994;
Original page
Keywords: Polish space | Suslin space | measurable space | Suslin family | (random) fixed point | (random) maximal element | (random) equilibria | (random) qualitative game | (random) generalized game | (random) variational inequality | (random) quasi-variational inequality | class L | L-majorized | measurable selection theorem | property (K) | random operator.
ABSTRACT
In this paper, existence theorems of random maximal elements, random equilibria for the random one-person game and random generalized game with a countable number of players are given as applications of random fixed point theorems. By employing existence theorems of random generalized games, we deduce the existence of solutions for non-compact random quasi-variational inequalities. These in turn are used to establish several existence theorems of noncompact generalized random quasi-variational inequalities which are either stochastic versions of known deterministic inequalities or refinements of corresponding results known in the literature.
