System Of Quasi-equilibrium Problems Research Articles

Existence of solutions for a system of quasi-variational relation problems and some applications

In this paper, we study the existence of solutions for a new class of systems of quasi-variational relation problems on different domains. As applications, we obtain existence theorems of solutions for systems of quasi-variational inclusions, systems of quasi-equilibrium problems, systems of generalized maximal element problems, systems of generalized KKM problems and systems of generalized quasi-Nash equilibrium problems on different domains. The results of this paper improve and generalize several known results on variational relation problems.

KKM Theorems in GFC-Spaces and the Application to the System of General Quasiequilibrium Problems

In this paper,new KKM theorems and a Browder type fixed point theorem are established for GFC-spaces.As applications,equilibrium existence theorems for the system of general quasiequilibrium problems and the system of quasiequilibrium problems are obtained in GFC-spaces.

Some results on systems of quasi-variational inclusion problems and systems of generalized quasi-variational inclusion problems

In this paper, we study systems of quasi-variational inclusion problem and systems of quasi-variational disclusion problem. From the existence theorems of solution for these two types of problems, we study various types of systems of quasi-variational inclusion problems, systems of quasi-equilibrium problems, systems of quasi-KKM theorem, abstract economics and system of KKM theorem. We also show their equivalent relations. We study further existence theorems of solution for generalized quasi-variational inclusion problem. Our results are different from any existence result in the literature.

Systems of quasi-equilibrium problems with lower and upper bounds

In this work, we consider systems of quasi-equilibrium problems with lower and upper bounds and establish the existence of their solutions by using some known maximal element theorems for a family of multivalued maps. Our problems are more general than the one posed in [G. Isac, V.M. Sehgal, S.P. Singh, An alternative version of a variational inequality, Indian J. Math. 41 (1999) 25–31]. As a particular case, we also get the answer to the problem raised in [G. Isac, V.M. Sehgal, S.P. Singh, An alternative version of a variational inequality, Indian J. Math. 41 (1999) 25–31].