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The conceptions of (generalized) Tykhonov well-posedness for generalized vector quasi-equilibrium problems, (generalized) Hadamard well-posedness for parametrically generalized vector quasi-equilibrium problems and (generalized) Tykhonov well-posedness for parametrical system of generalized vector quasi-equilibrium problems are introduced. The metric characterizations and/or sufficient criteria of the proposed well-posedness are presented, and the relations between (generalized) Tykhonov well-posedness for generalized vector quasi-equilibrium problems and that for constrained minimizing problems are discussed. Finally, the relations among several types of the well-posedness are exhibited in detail.

Several types of well-posedness for generalized vector quasi-equilibrium problems with their relations