Multitime multiobjective variational problems and vector variational-like inequalities

•Multitime multiobjective variational problem has been taken.•Introduce the new class of vector variational-like inequalities.•Invexities for multitime functional have been constructed.•Derive relations of introduced inequalities with considered variational problem.

In this paper, we introduce vector variational-like inequality with its weak formulation for multitime multiobjective variational problem. Moreover, we establish the relationships between the solutions of introduced inequalities and (properly) efficient solutions of multitime multiobjective variational problem, involving the invexities of multitime functionals. Some examples are provided to illustrate our results.