Solutions existence for two types of mixed variational relation problems.

In the last decade, more and more authors have attempted to treat in a unified manner, by means of some binary or ternary relations, various equilibrium or quasi-equilibrium problems encountered in literature. Several types of variational relation problems have been investigated in many recent papers in which, as for other mathematical models, the main focus has been on sufficient conditions for the existence of solution. The existence of solution has been also studied for several types of systems of two variational relation problems called either mixed variational relation problems or simultaneous variational relation problems. In this paper, we deal with the existence of solutions for two types of mixed variational relation problems in which the involved relations (one binary and the other ternary) are linked by a certain condition of compatibility. [ABSTRACT FROM AUTHOR]