Thu Dau Mot University Journal of Science


On the lower semicontinuity of the solution mapping for parametric vector mixed quasivariational inequality problem of the Minty type

By Nguyen Van Hung, Vo Viet Tri
DOI: 10.37550/tdmu.EJS/2020.02.041

Abstract

In this paper, we study a class of parametric vector mixed quasivariational
inequality problem of the Minty type (in short, (MQVIP)). Afterward, we
establish some sufficient conditions for the stability properties such as the
inner-openness, lower semicontinuity and Hausdorff lower semicontinuity of
the solution mapping for this problem. The results presented in this paper
is new and wide to the corresponding results in the literature


Full text

View PDF

References

[1] L.Q. Anh, N.V. Hung, (2018). Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems, J. Ind.
Manag. Optim.
, 14, 65{79.
[2] J.P. Aubin, I. Ekeland, (1984).
Applied Nonlinear Analysis, John Wiley and
Sons, New York.
[3] F. Giannessi, (1980).
Theorems of alternative, quadratic programmes and complementarity problems, in: R. W. Cottle, F. Giannessi, J. L. Lions (Eds.), Variational Inequalities and Complementarity Problems, Wiley, Chichester, 151-186.
[4] N.V. Hung, (2013). Stability of a solution set for parametric generalized vector
mixed castration inequality problem,
J. Inequal. Appl., 276, 1{13.
[5] N.V. Hung, (2018). On the stability of the solution mapping for parametric
traffic network problems,
Indag. Math., 29, 885-894.
[6] N.V. Hung, N.M. Hai, (2019). Stability of approximating solutions to parametric bilevel vector equilibrium problems and applications,
Comput. Appl. Math.,
38, 1{17.
[7] P.Q. Khanh, D.T. Luc, (2008). Stability of solutions in parametric variational
relation problems,
Set-Valued Anal., 16, 1015{1035.
[8] C.S. Lalitha, G. Bhatia, (2011). Stability of parametric quasivariational inequality of the Minty type,
J. Optim. Theory Appl., 148 , 281{300.
[9] R.T. Rockafellar, R. J-B. Wets, (1998).
Variational Analysis, Springer, Berlin
Heidelberg, .
[10] J. Zhao, (1997). The lower semicontinuity of optimal solution sets,
J. Math.
Anal. Appl.
, 207, 240-254.






Publication Information

Publisher

Thu Dau Mot University, Viet Nam

Honorary Editor-in-Chief and Chairman of the Editorial Board

Assoc. Prof. Nguyen Van Hiep

Deputy Editor-in-Chief

PhD. Trần Hạnh Minh Phương
Thu Dau Mot University

Editorial Board

Prof. Tran Van Doan
Fujen University, Taiwan
Prof. Zafar Uddin Ahmed
Vietnam National University Ho Chi Minh City

Prof.Dr. Phillip G.Cerny
The University of Manchester, United Kingdom
Prof. Ngo Van Le
University of Social Sciences and Humanities (VNU-HCM)

Prof. Bui The Cuong
Southern Institute of Social Sciences​​​​​​​
Prof. Le Quang Tri
Can Tho University

Assoc. Prof. Nguyen Van Duc
Animal Husbandry Association of Vietnam
Assoc. Prof. Ted Yuchung Liu
National Pingtung University, Taiwan

PhD. Anita Doraisami
Economics Monash University, Australia
Prof. Dr. Andrew Seddon
Asia Pacific University of Technology & innovation (APU)

Assoc. Prof. Le Tuan Anh
Thu Dau Mot University
Prof. Abtar Darshan Singh
Asia Pacific University, Malaysia

Prof.Dr. Ron W.Edwards
The University of Melbourne, Australia
Assoc. Prof. Hoang Xuan Nien
Thu Dau Mot University

PhD. Nguyen Duc Nghia
Vietnam National University Ho Chi Minh City
PhD. Bao Dat
Monash University (Australia)

PhD. Raqib Chowdhury
Monash University (Australia)
PhD. Nguyen Hoang Tuan
Thu Dau Mot University

PhD. Nguyen Thi Lien Thuong
Thu Dau Mot University

Assistant

Nguyen Thi Man
Thu Dau Mot University