JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON A SYSTEM OF GENERALIZED NONLINEAR VARIATIONAL INEQUALITIES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON A SYSTEM OF GENERALIZED NONLINEAR VARIATIONAL INEQUALITIES
Li, Jingchang; Guo, Zhenyu; Liu, Zeqing; Kang, Shin-Min;
  PDF(new window)
 Abstract
In this paper a new class of system of generalized nonlinear variational inequalities involving strongly monotone, relaxed co coercive and relaxed generalized monotone mappings in Hilbert spaces is introduced and studied. Based on the projection method, an equivalence between the system of generalized nonlinear variational inequalities and the fixed point problem is established, which is used to suggest some new iterative algorithms for computing approximate solutions of the system of generalized nonlinear variational inequalities. A few sufficient conditions which ensure the existence and uniqueness of solution of the system of generalized nonlinear variational inequalities are given, and the convergence analysis of iterative sequences generated by the algorithms are also discussed.
 Keywords
system of generalized nonlinear variational inequalities;iterative algorithms;solution;convergence;
 Language
English
 Cited by
 References
1.
T. Cai, Z. Liu, and S. M. Kang, Existence of solutions for a system of generalized non-linear implicit variational inequalities, Math. Sci. Res. J. 8 (2004), no. 6, 176-183

2.
L. S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995), 114-125 crossref(new window)

3.
Z. Liu, Y. Hao, S. K. Lee, and S. M. Kang, On a system of general quasivariational like inequalities, Math. Sci. Res. J. 15 (2005), no. 2, 29-38

4.
H. Z. Nie, Z. Liu, K. H. Kim, and S. M. Kang, A system of nonlinear variational inequalities involving strongly monotone and pseudocontractive mappings, Adv. Nonlinear Var. Inequal. 6 (2003), no. 2, 91-99

5.
R. U. Verma, Approximation-solvability of a new system of nonlinear quasivariational inequalities, Adv. Nonlinear Var. Inequal.3 (2000), 47-60

6.
R. U. Verma, Computational role of partially relaxed monotone mappings in solvability of a system of nonlinear variational inequalities, Adv. Nonlinear Var. Inequal. 3 (2000), 79-86

7.
R. U. Verma, Iterative algorithms and a new system of nonlinear quasivaritional inequalities, Adv. Nonlinear Var. Inequal.4 (2001), 117-124

8.
R. U. Verma, Projection methods, algorithms, and a new system of nonlinear variational inequalities, Computers Math. Applic. 41 (2001), 1025-1031 crossref(new window)

9.
Q. H Wu, Z. Liu, S. H. Shim, and S. M. Kang, Approximation-solvability of a new system of nonlinear variational inequalities, Math. Sci. Res. J. 7 (2003), no. 8, 338-346