Comp. Appl. Math. DOI 10.1007/s40314-016-0411-z Stability of solution mappings for parametric bilevel vector equilibrium problems Lam Quoc Anh 1 · Nguyen Van Hung 2,3 Received: 28 February 2016 / Revised: 29 June 2016 / Accepted: 9 December 2016 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016 Abstract In this paper, we first revisit the parametric bilevel vector equilibrium problems in Hausdorff topological vector spaces. Then we study the stability conditions such as (Hausdorff) upper semicontinuity, (Hausdorff) lower semicontinuity, outer-continuity and outer-openness of solutions for such problems. Many examples are provided to illustrate the essentialness of the imposed assumptions. For the applications, we obtain the stability results for the parametric vector variational inequality problems with equilibrium constraints and parametric vector optimization problems with equilibrium constraints. Keywords Bilevel vector equilibrium problem · Variational inequality with equilibrium constraints · Optimization problems with equilibrium constraints · Upper (lower) semicontinuity · Outer-continuity · Outer-openness Mathematics Subject Classification 90C31 · 49J40 · 49J53 1 Introduction Equilibrium problem was first introduced and investigated by Blum and Oettli (1994). Then this problem has been focused and intensively studied in many topics such as the existence of solutions, the stability of solutions and the (unique) well posedness of approximate solutions Communicated by José Mario Martínez. B Nguyen Van Hung nguyenvanhung2@tdt.edu.vn Lam Quoc Anh quocanh@ctu.edu.vn 1 Department of Mathematics, Teacher College, Can Tho University, Can Tho, Vietnam 2 Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam 3 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam 123