Abstract
We explore the solvability of a general system of nonlinear relaxed cocoercive variational inequality (SNVI) problems based on a new projection system for the direct product of two nonempty closed and convex subsets of real Hilbert spaces.
Download the article in PDF format (size 96 Kb)
| 2000 Mathematics Subject Classification:
primary 49J40, 65B05; secondary 47H20
|
| (Metadata: XML, RSS, BibTeX) |
MathSciNet:
MR2376??? |
References
-
S. S. Chang, Y. J. Cho and J. K. Kim, “On the two-step projection methods and applications to variational inequalities”, Math. Inequal. Appl., accepted.
MR2358662
-
L. S. Liu, “Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces”, J. Math. Anal. Appl. 194 (1995) 114–127.
MR1353071
-
Z. Liu, J. S. Ume and S. M. Kang, “Generalized nonlinear variational-like inequalities in reflexive Banach spaces”, J. Optim. Theory Appl. 126 (2005) 157–174.
MR2158437
-
H. 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) 91–99.
MR1978396
-
R. U. Verma, “Nonlinear variational and constrained hemivariational inequalities”, ZAMM: Z. Angew. Math. Mech. 77 (1997) 387–391.
MR1455359
-
R. U. Verma, “Projection methods, algorithms and a new system of nonlinear variational inequalities”, Comput. Math. Appl. 41 (2001) 1025–1031.
MR1826902
-
R. U. Verma, “Generalized convergence analysis for two-step projection methods and applications to variational problems”, Appl. Math. Lett. 18 (2005) 1286–1292.
MR2170885
-
R. Wittmann, “Approximation of fixed points of nonexpansive mappings”, Arch. Math. (Basel) 58 (1992) 486–491.
MR1156581
-
E. Zeidler, Nonlinear Functional Analysis and its Applications II/B (Springer-Verlag, New York, 1990).
MR1033498
|
