JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A NEW SYSTEM OF GENERALIZED NONLINEAR MIXED QUASIVARIATIONAL INEQUALITIES AND ITERATIVE ALGORITHMS IN HILBERT SPACES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A NEW SYSTEM OF GENERALIZED NONLINEAR MIXED QUASIVARIATIONAL INEQUALITIES AND ITERATIVE ALGORITHMS IN HILBERT SPACES
Kim, Jong-Kyu; Kim, Kyung-Soo;
  PDF(new window)
 Abstract
We introduce a new system of generalized nonlinear mixed quasivariational inequalities and prove the existence and uniqueness of the solution for the system in Hilbert spaces. The main result of this paper is an extension and improvement of the well-known corresponding results in Kim-Kim [16], Noor [21]-[23] and Verma [24]-[26].
 Keywords
a system of generalized nonlinear mixed quasivariational inequalities;iterative sequence with errors;algorithm;
 Language
English
 Cited by
1.
On the hierarchical variational inclusion problems in Hilbert spaces, Fixed Point Theory and Applications, 2013, 2013, 1, 179  crossref(new windwow)
2.
Weak convergence of algorithms for asymptotically strict pseudocontractions in the intermediate sense and equilibrium problems, Fixed Point Theory and Applications, 2012, 2012, 1, 132  crossref(new windwow)
3.
A New Method for Solving Monotone Generalized Variational Inequalities, Journal of Inequalities and Applications, 2010, 2010, 1, 657192  crossref(new windwow)
4.
Solution sensitivity of generalized nonlinear parametric (A,η,m)-proximal operator system of equations in Hilbert spaces, Journal of Inequalities and Applications, 2014, 2014, 1, 362  crossref(new windwow)
5.
An Iteration Method for Common Solution of a System of Equilibrium Problems in Hilbert Spaces, Fixed Point Theory and Applications, 2011, 2011, 1, 780764  crossref(new windwow)
6.
Perturbed Mann iterative method with errors for a new system of generalized nonlinear variational-like inclusions, Mathematical and Computer Modelling, 2010, 51, 1-2, 63  crossref(new windwow)
7.
Convergence theorems for common solutions of various problems with nonlinear mapping, Journal of Inequalities and Applications, 2014, 2014, 1, 2  crossref(new windwow)
 References
1.
C. Baiocchi and A. Caopelo, Variational and quasivariational inequalities, John Wiley & Sons, Inc., New York, 1984

2.
A. Bensounssan and J. L. Lions, Impulse Control and Quasivariational Inequalities, Gauthiers-Villers, Bordas, Paris, 1984

3.
H. Brezis, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Publishing Co., Amsterdam-London, 1973

4.
S. S. Chang, J. K. Kim, and K. H. Kim, On the existence and iterative approximation problems of solutions for set-valued variational inclusions in Banach spaces, J. Math. Anal. Appl. 268 (2002), no. 1, 89-108 crossref(new window)

5.
S. S. Chang, J. K. Kim, and Y. M. Nam, Multivalued quasi-variational inclusions and multivalued accretive equations, Comput. Math. Appl. 48 (2004), no. 10-11, 1441-1452 crossref(new window)

6.
Y. P. Fang, N. J. Huang, and J. K. Kim, A system of multi-valued generalized order complementarity problems in ordered metric spaces, Z. Anal. Anwendungen 22 (2003), no. 4, 779-788

7.
Y. P. Fang, N. J. Huang, and J. K. Kim, Existence results for systems of vector equilibrium problems, J. Global Optim. 35 (2006), no. 1, 71-83 crossref(new window)

8.
F. Giannessi and A. Maugeri, Variational Inequalities and Network Equilibrium Problems, Plenum Press, New York, 1995

9.
R. Glowinski and P. Le Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, SIAM Publication Co., Philadelphia, 1989

10.
N. J. Huang, Generalized nonlinear variational inclusions with noncompact valued mapping, Appl. Math. Lett. 9 (1996), no. 3, 25-29

11.
N. J. Huang, On the generalized implicit quasivariational inequalities, J. Math. Anal. Appl. 216 (1997), no. 1, 197-210 crossref(new window)

12.
N. J. Huang, Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasivariational inclusions, Comput. Math. Appl. 35 (1998), no. 10, 1-7

13.
N. J. Huang, A new completely general class of variational inclusions with noncompact valued mappings, Comput. Math. Appl. 35 (1998), no. 10, 9-14

14.
N. J. Huang, Y. P. Liu, Y. Y. Tang, and M. R. Bai, The generalized set-valued strongly nonlinear implicit variational inequalities, Comput. Math. Appl. 37 (1999), no. 10, 29-36 crossref(new window)

15.
N. J. Huang, M. R. Bai, Y. J. Cho, and S. M. Kang, Generalized nonlinear mixed quasi-variational inequalities, Comput. Math. Appl. 40 (2000), no. 2-3, 205-215 crossref(new window)

16.
J. K. Kim and D. S. Kim, A new system of generalized nonlinear mixed variational inequalities in Hilbert spaces, J. Convex Anal. 11 (2004), no. 1, 235-243

17.
J. K. Kim, Y. M. Nam, N. J. Huang, and H. Dong, On generalized vector variational inequalities with set-valued mappings, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 13 (2006), no. 2, 221-230

18.
J. K. Kim, K. H. Kim, and K. S. Kim, Set-valued quasivariational inclusions and implicit resolvent equations in Banach spaces, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 11 (2004), no. 4, 491-502

19.
H. Y. Lan, J. K. Kim, and N. J. Huang, On the generalized nonlinear quasi-variational inclusions involving non-monotone set-valued mappings, Nonlinear Funct. Anal. and Appl. 9 (2004), no. 3, 451-465

20.
J. Li, N. J. Huang, and J. K. Kim, On implicit vector equilibrium problems, J. Math. Anal. Appl. 283 (2003), no. 2, 501-512 crossref(new window)

21.
M. A. Noor, Set-valued quasivariational inclusions, Korean J. Comput. Appl. Math. 7 (2000), no. 1, 101-113

22.
M. A. Noor, K. I. Noor, and Th. M. Rassias, Set-valued resolvent equations and mixed variational inequalities, J. Math. Anal. Appl. 220 (1998), no. 2, 741-759 crossref(new window)

23.
M. A. Noor, K. I. Noor, and Th. M. Rassias, Some aspects of variational inequalities, J. Comput. Appl. Math. 47 (1993), no. 3, 285-312 crossref(new window)

24.
R. U. Verma, On a new system of nonlinear variational inequalities and associated iterative algorithms, Math. Sci. Res. Hot-Line 3 (1999), no. 8, 65-68

25.
R. U. Verma, Projection methods, Algorithms and a new system of nonlinear variational inequalities, Compu. Math. Appl. 41 (2001), no. 7-8, 1025-1031 crossref(new window)

26.
R. U. Verma, Iterative algorithms and a new system of nonlinear quasivariational inequalities, Adv. Nonlinear Var. Inequal. 4 (2001), no. 1, 117-124