ALGORITHMS FOR SYSTEMS OF NONLINEAR VARIATIONAL INEQUALITIES

Title & Authors
ALGORITHMS FOR SYSTEMS OF NONLINEAR VARIATIONAL INEQUALITIES
Cho, Y.J.; Fang, Y.P.; Huang, N.J.; Hwang, H.J.;

Abstract
In this paper, we introduce and study a new system of nonlinear variational inequalities. The existence and uniqueness of solution for this problem are proved and an iterative algorithm for approximating the solution of system of nonlinear variational inequalities is constructed.
Keywords
system of nonlinear variational inequalities;iterative algorithm;resolvent operator;existence and convergence;
Language
English
Cited by
1.
SYSTEM OF MIXED VARIATIONAL INEQUALITIES IN REFLEXIVE BANACH SPACES,;;

Journal of applied mathematics & informatics, 2009. vol.27. 3_4, pp.693-702
1.
Approximation solvability of a class of nonlinear set-valued variational inclusions involving (A,η)-monotone mappings, Journal of Mathematical Analysis and Applications, 2008, 337, 2, 969
2.
The existence and uniqueness of solution and the convergence of a multi-step iterative algorithm for a system of variational inclusions with (A, η, m)-accretive operators, Journal of Global Optimization, 2007, 39, 3, 441
3.
Convergence and stability of iterative algorithm for a new system of (A,η)-accretive mapping inclusions in Banach spaces, Computers & Mathematics with Applications, 2008, 56, 9, 2305
4.
Iterative approximation of a unique solution of a system of variational-like inclusions in real -uniformly smooth Banach spaces, Nonlinear Analysis: Theory, Methods & Applications, 2007, 67, 3, 917
5.
System of General Variational Inequalities Involving Different Nonlinear Operators Related to Fixed Point Problems and Its Applications, Fixed Point Theory and Applications, 2011, 2011, 1
6.
System of generalized variational inclusions with H-accretive operators in uniformly smooth Banach spaces, Journal of Computational and Applied Mathematics, 2009, 230, 2, 424
7.
New perturbed finite step iterative algorithms for a system of extended generalized nonlinear mixed quasi-variational inclusions, Computers & Mathematics with Applications, 2010, 60, 11, 2953
8.
On a new system of generalized mixed quasi-variational-like inclusions with -accretive operators in real -uniformly smooth Banach spaces, Nonlinear Analysis: Theory, Methods & Applications, 2008, 68, 4, 981
9.
General system of (A,η)-maximal relaxed monotone variational inclusion problems based on generalized hybrid algorithms, Communications in Nonlinear Science and Numerical Simulation, 2010, 15, 2, 238
10.
An iterative algorithm for a system of generalized implicit variational inclusions, SpringerPlus, 2016, 5, 1
11.
Iterative algorithm with mixed errors for solving a new system of generalized nonlinear variational-like inclusions and fixed point problems in Banach spaces, Chinese Annals of Mathematics, Series B, 2013, 34, 4, 593
12.
System of set-valued mixed quasi-variational-like inclusions involving H-η-monotone operators in Banach spaces, Applied Mathematics and Mechanics, 2009, 30, 1, 1
13.
A new system of variational inclusions with ( H, η)-monotone operators, Bulletin of the Australian Mathematical Society, 2006, 74, 02, 301
14.
Existence and iterative approximation of solutions of a system of general variational inclusions, Applied Mathematics and Computation, 2009, 215, 1, 110
15.
Algorithms for solutions of extended general mixed variational inequalities and fixed points, Optimization Letters, 2013, 7, 8, 1929
16.
--Accretive Mappings and a New System of Generalized Variational Inclusions with --Accretive Mappings in Banach Spaces, ISRN Applied Mathematics, 2011, 2011, 1
17.
A system of variational inclusions with Pη-accretive operators, Journal of Computational and Applied Mathematics, 2008, 216, 1, 198
18.
A system of generalized variational inclusions involving generalized H(·,·)-accretive mapping in real q-uniformly smooth Banach spaces, Applied Mathematics and Computation, 2011, 217, 23, 9679
19.
Resolvent algorithms for system of generalized nonlinear variational inclusions and fixed point problems, Afrika Matematika, 2014, 25, 4, 1023
20.
Iterative Algorithms for New General Systems of Set-Valued Variational Inclusions Involving(A,η)-Maximal Relaxed Monotone Operators, Journal of Applied Mathematics, 2014, 2014, 1
21.
Stability of iterative processes with errors for a system of nonlinear (A,η)-accretive variational inclusions in Banach spaces, Computers & Mathematics with Applications, 2008, 56, 1, 290
22.
General system of -monotone variational inclusion problems based on generalized hybrid iterative algorithm, Nonlinear Analysis: Hybrid Systems, 2007, 1, 3, 326
23.
A new system of generalized nonlinear co-complementarity problems, Journal of Applied Mathematics and Computing, 2006, 21, 1-2, 379
24.
The p-step iterative algorithm for a system of generalized mixed quasi-variational inclusions with (H,η)-monotone operators, Journal of Global Optimization, 2007, 38, 3, 387
25.
Existence and stability of iterative algorithms for the system of nonlinear quasi-mixed equilibrium problems, Applied Mathematics Letters, 2011, 24, 3, 308
26.
Three-step iterative algorithm for a system of set-valued variational inclusions with -monotone operators, Nonlinear Analysis: Theory, Methods & Applications, 2008, 68, 1, 139
27.
Graph Convergence for the $$H(\cdot ,\cdot )$$ H ( · , · ) -Co-accretive Mapping with an Application, Bulletin of the Malaysian Mathematical Sciences Society, 2015, 38, 4, 1481
28.
A new system of generalized mixed quasi-variational inclusions with (H,η)-monotone operators, Journal of Mathematical Analysis and Applications, 2007, 327, 1, 175
29.
SYSTEM OF GENERALIZED NONLINEAR MIXED VARIATIONAL INCLUSIONS INVOLVING RELAXED COCOERCIVE MAPPINGS IN HILBERT SPACES, East Asian mathematical journal , 2015, 31, 3, 383
30.
Existence and Stability of Iterative Algorithm for a System of Random Set-Valued Variational Inclusion Problems Involving (A,m,η)-Generalized Monotone Operators, Journal of Applied Mathematics, 2012, 2012, 1
31.
On a new system of nonlinear A-monotone multivalued variational inclusions, Journal of Mathematical Analysis and Applications, 2007, 327, 1, 481
References
1.
J. Math. Anal. Appl., 1996. vol.201. pp.609-630

2.
Appl. Math. Series, 1974.

3.
Appl. Math. Lett., 1999. vol.12. pp.69-76

4.
Application to Free Boundary Problems, 1984.

5.
Operateurs Maximaux Monotone et Semigroups de Contraction dans les Espaces de Hilbert, 1973.

6.
Comput. Math. Appl., 1999. vol.37. pp.17-24

7.
Appl. Math. Comput., 2000. vol.113. pp.67-80

8.
J. Math. Anal. Appl., 1997. vol.210. pp.88-101

9.
Variational Inequalities and Network Equilibrium Problems, 1995.

10.
Numerical Analysis of Variational Inequalities, 1981.

11.
J. Math. Anal. Appl., 1994. vol.185. pp.706-712

12.
Appl. Math. Lett., 1996. vol.9. 3, pp.25-29

13.
Comput. Math. Appl., 1998. vol.35. 6, pp.9-14

14.
J. Math. Anal. Appl., 2001. vol.256. pp.345-359

15.
Fixed point theorems and a new system of multivalued generalized order complimentarity problems, 0000.

16.
Publ. Math. Debrecen, 2000. vol.56. pp.185-195

17.
J. Math. Anal. Appl., 1997. vol.209. pp.572-584

18.
New Zealand J. Math., 1997. vol.26. pp.53-80;229-255

19.
Math. Comput. Modelling, 1997. vol.26. 7, pp.29-34

20.
Inequality Problems in Mechanics and Applications, 1980.

21.
J. Math. Anal. Appl., 1992. vol.116. pp.386-392

22.
Math. Ineq. Appl., 0000. vol.4. pp.443-453

23.
J. Comput. Anal. Appl., 0000. vol.4. pp.129-139

24.
Comput. Appl. Math., 0000. vol.41. pp.1025-1031

25.
J. Math. Anal. Appl., 0000. vol.158. pp.139-160

26.
KKM Theory and Applicaions in Nonlinear Analysis, 1999.