ANZIAM J. 49 (2007), no. 2, pp. 205–212.

General projection systems and relaxed cocoercive nonlinear variational inequalities

Ram U. Verma
Department of Mathematics
University of Toledo
Ohio 43606
Received 8 April, 2007


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.

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2000 Mathematics Subject Classification: primary 49J40, 65B05; secondary 47H20
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2376???


  1. 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
  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) 114–127. MR1353071
  3. 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
  4. 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
  5. R. U. Verma, “Nonlinear variational and constrained hemivariational inequalities”, ZAMM: Z. Angew. Math. Mech. 77 (1997) 387–391. MR1455359
  6. R. U. Verma, “Projection methods, algorithms and a new system of nonlinear variational inequalities”, Comput. Math. Appl. 41 (2001) 1025–1031. MR1826902
  7. R. U. Verma, “Generalized convergence analysis for two-step projection methods and applications to variational problems”, Appl. Math. Lett. 18 (2005) 1286–1292. MR2170885
  8. R. Wittmann, “Approximation of fixed points of nonexpansive mappings”, Arch. Math. (Basel) 58 (1992) 486–491. MR1156581
  9. E. Zeidler, Nonlinear Functional Analysis and its Applications II/B (Springer-Verlag, New York, 1990). MR1033498
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