Existence Theorems for a Variational Relation Problem

ABSTRACT

The aim of this article is to establish new existence results for a certain type of variational relation problem studied by Agarwal et al. in a very recent article. This problem is a general model for several quasivariational inclusions and quasiequilibrium problems investigated in many recent articles. The main tools in proving the existence theorems are two well-known fixed point theorems (Eilenberg-Montgomery and Kakutany-Fan Glicksberg, respectively). In the last section, we prove that, applied in special cases, our results are different or stronger than several earlier results.

KEYWORDS:

• Fixed point
• quasivariational inclusion
• set-valued mapping
• variational relation problem

MATHEMATICS SUBJECT CLASSIFICATION:

• 49J40
• 49J53