AN ITERATIVE METHOD FOR NONLINEAR MIXED IMPLICIT VARIATIONAL INEQUALITIES

  • JEONG, JAE UG (Department of Mathematics, Dong Eui University)
  • Received : 2004.07.27
  • Accepted : 2004.09.10
  • Published : 2004.12.25

Abstract

In this paper, we develop an iterative algorithm for solving a class of nonlinear mixed implicit variational inequalities in Hilbert spaces. The resolvent operator technique is used to establish the equivalence between variational inequalities and fixed point problems. This equivalence is used to study the existence of a solution of nonlinear mixed implicit variational inequalities and to suggest an iterative algorithm for solving variational inequalities. In our results, we do not assume that the mapping is strongly monotone.

Keywords

Variational inequality;resolvent operator;iterative algorithm

Acknowledgement

Supported by : Dong Eui University

References

  1. Operateur Maximaux Monotones et Semigroupes de Contractions dans les Espaces de Hilbert Brezis, H.
  2. J. Math. Anal. Appl. v.185 A perturbed algorithm for variational inclusions Hassouni, A.;Moudafi, A.
  3. Nonlinear Mappings of Monotone Type Pascali, D.;Sburlan, S.