A continuous-time version of the multivariate stopping problem is considered. Associated with vector valued jump stochastic processes, stopping problems with a monotone logical rule are defined under the notion of Nash equilibrium point. The existence of an equilibrium strategy and its characterization by integral equations are obtained. Illustrative examples are provided.

In this paper, employing the Ky Fan section theorem,we give a class of Ky Fan inequality for set-valued maps,usually it takes Ky Fan inequality ,vector equilibrium problems as its special cases.

We prove an invariance principle for a vector-valued additive functional of a Markov chain for almost every starting point with respect to an ergodic equilibrium distribution. The hypothesis is a moment bound on the resolvent.

The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of subsets of the same space de…ned by means of vector-valued functions. These Farkas-type results are used to derive characterizations of the weak solutions of vector optimization problems (including ...

In this paper, we introduce the concept of generalized relaxed αpseudomonotonicity for vector valued bi-functions. By using the KKM technique, we obtain some substantial results of the vector equilibrium problems with generalized relaxed α-pseudomonotonicity assumptions in reflexive Banach spaces. Several examples are provided to illustrate our investigations.

We apply an existence theorem of variational inclusion problem on metric spaces to study optimization problems, set-valued vector saddle point problems, bilevel problems, and mathematical programs with equilibrium constraint on metric spaces. We study these problems without any convexity and compactness assumptions. Our results are different from any existence results of these types of problems...

‎In this paper‎, ‎we introduce and study a class of generalized vector quasi-equilibrium problem‎, ‎which includes many vector equilibrium problems‎, ‎equilibrium problems‎, ‎vector variational inequalities and variational inequalities as special cases‎. ‎Using one person game theorems‎, ‎the concept of escaping sequences and without convexity assumptions‎, ‎we prove some existence results for ...