[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2018.26.2.299

SOLUTIONS OF VECTOR VARIATIONAL INEQUALITY PROBLEMS

Salahuddin, Salahuddin (Department of Mathematics Jazan University)

Publication Information

Korean Journal of Mathematics / v.26, no.2, 2018 , pp. 299-306 More about this Journal

Abstract

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

Keywords

Vector variational inequality problems; ${\parallel}{\cdot}{\parallel}$ -sequentially continuous; Solution; sequences; Banach spaces;

Citations & Related Records

Reference

1	Ravi P. Agarwal, M. K. Ahmad and Salahuddin, Hybrid type generalized multivalued vector complementarity problems, Ukrainian Math. J., 65 (1) (2013), 6-20.
2	G. A. Anastassiou and Salahuddin, Weakly set valued generalized vector variational inequalities, J. Computat. Anal. Appl. 15 (4) (2013), 622-632.
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.
4	S. S. Chang, Fixed Point Theory with Applications, Chongquing Publishing House, Chongqing, 1984.
5	S. S. Chang, Variational Inequalities and Complementarity Problems, Theory with Applications, Shanghai Scientiﬁc and Tech. Literature Publishing House, Shanghai, 1991.
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. DOI
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. DOI
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.
9	K. Fan, Some properties of convex sets related to ﬁxed point theorems, Math. Ann. 266 (4) (1984), 519-537. DOI
10	F. Ferro, A minimax theorem for vector valued functions, J. Optim. Theory Appl. 60 (1989), 19-31. DOI
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.
12	G. Hartmann and G. Stampacchia, On some nonlinear elliptic differential functional equations, Acta Math. 115 (1966), 271-310. DOI
13	S. Laszlo, Some existence results of solutions for general variational inequalities, J. Optim. Theory Appl., 150 (2011), 425-443. DOI
14	Salahuddin, General set valued vector variational inequality problems, Commun. Optim. Theory, Article ID 13 (2017), 1-16.
15	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.
16	B. S. Lee and Salahuddin, Minty lemma for inverted vector variational inequalities, Optimization 66 (3) (2017), 351-359. DOI
17	V. D. Radulescu, Qualitative analysis of nonlinear elliptic partial differential equations: Monotonicity Analysis and Variational Methods, Hindawi Publishing Corporation, New York, 2008.
18	Salahuddin, Generalized vector quasi variational type inequalities, Trans. Math. Prog. Appl. 1 (12) (2013), 51-64.