Korean J. Math. Vol. 26 No. 2 (2018) pp.299-306
DOI: https://doi.org/10.11568/kjm.2018.26.2.299

Solutions of vector variational inequality problems

Main Article Content

Dr. Salahuddin

Abstract

In this paper, we prove the existence results of the solutions for {\it vector variational inequality problems} by using the $\|\cdot\|$-sequentially continuous mapping.



Article Details

References

[1] Ravi P. Agarwal, M. K. Ahmad and Salahuddin, Hybrid type generalized multivalued vector complementarity problems, Ukrainian Math. J., 65 (1) (2013), 6–20. Google Scholar

[2] G. A. Anastassiou and Salahuddin, Weakly set valued generalized vector variational inequalities, J. Computat. Anal. Appl. 15 (4) (2013), 622–632. Google Scholar

[3] M. Fabian. P. Habala, P. Hajek, V. Monlesinos Santalucia, J. Lelant and V. Zizler, Variational Analysis and Infinite Dimensional Geometry, Springer-Verlag, New york, 2001. Google Scholar

[4] S. S. Chang, Fixed Point Theory with Applications, Chongquing Publishing House, Chongqing, 1984. Google Scholar

[5] S. S. Chang, Variational Inequalities and Complementarity Problems, Theory with Applications, Shanghai Scientific and Tech. Literature Publishing House, Shanghai, 1991. Google Scholar

[6] S. S. Chang, G. Wang and Salahuddin, On the existence theorems of solutions for generalized vector variational inequalities, J. Inequal. Appl. (2015), 2015:365. Google Scholar

[7] G. Y. Chen, Existence of solutions for a vector variational inequalities: An extension of Hartman-Stampacchia theorems, J. Optim. Theory Appl. 74 (3) (1992), 445–456. Google Scholar

[8] X. P. Ding and Salahuddin, Generalized mixed general vector variational like inequalities in topological vector spaces, J. Nonlinear Anal. Optim. 4 (2) (2013), 163–172. Google Scholar

[9] K. Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (4) (1984), 519–537. Google Scholar

[10] F. Ferro, A minimax theorem for vector valued functions, J. Optim. Theory Appl. 60 (1989), 19–31. Google Scholar

[11] F. Giannessi, Theorems of alternative, quadratic programs and complementarity problems: In R. W. Cottle, F. Giannessi and J. L. Lions (Eds) Variational Inequalities and Complementarity Problems, John Wiley and Sons, Chinchester. (1980), 151–186. Google Scholar

[12] G. Hartmann and G. Stampacchia, On some nonlinear elliptic differential func- tional equations, Acta Math. 115 (1966), 271–310. Google Scholar

[13] S. Laszlo, Some existence results of solutions for general variational inequalities, J. Optim. Theory Appl., 150 (2011), 425–443. Google Scholar

[14] B. S. Lee, M. F. Khan and Salahuddin, Hybrid type set valued variational like inequalities in reflexive Banach spaces, J. Appl. Math. Informatics. 27 (5-6) (2009), 1371–1379. Google Scholar

[15] B. S. Lee and Salahuddin, Minty lemma for inverted vector variational inequalities, Optimization 66 (3) (2017), 351–359. Google Scholar

[16] V. D. Radulescu, Qualitative analysis of nonlinear elliptic partial differential equations: Monotonicity Analysis and Variational Methods, Hindawi Publishing Corporation, New York, 2008. Google Scholar

[17] Salahuddin, Generalized vector quasi variational type inequalities, Trans. Math. Prog. Appl. 1 (12) (2013), 51–64. Google Scholar

[18] Salahuddin, General set valued vector variational inequality problems, Commun. Optim. Theory, Article ID 13 (2017), 1–16. Google Scholar