We consider vector equilibrium problems in real Banach spaces and study their regularized problems. Based on cone continuity and generalized convexity properties of vector-valued mappings, we propose general conditions that guarantee existence of solutions to such problems in cases of monotonicity and nonmonotonicity. First, our study indicates that every Tikhonov trajectory converges to a solution to the original problem. Then, we establish the equivalence between the problem solvability and the boundedness of any Tikhonov trajectory. Finally, the convergence of the Tikhonov trajectory to the least-norm solution of the original problem is discussed.

我们考虑实际Banach空间中的向量平衡问题，并研究它们的正规化问题。基于向量值映射的锥连续性和广义凸性，我们提出了保证单调性和非单调性情况下此类问题的解的存在的一般条件。首先，我们的研究表明，每个Tikhonov轨迹都收敛到原始问题的解决方案。然后，我们建立了问题可解性与任何Tikhonov轨迹的有界性之间的等价关系。最后，讨论了Tikhonov轨迹到原始问题的最小范数解的收敛性。