Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON A SYSTEM OF GENERALIZED NONLINEAR VARIATIONAL INEQUALITIES

  • Li, Jingchang (DALIAN VOCATIONAL TECHNICAL COLLEGE) ;
  • Guo, Zhenyu (DEPARTMENT OF MATHEMATICS LIAONING NORMAL UNIVERSITY) ;
  • Liu, Zeqing (DEPARTMENT OF MATHEMATICS LIAONING NORMAL UNIVERSITY) ;
  • Kang, Shin-Min (DEPARTMENT OF MATHEMATICS AND RESEARCH INSTITUTE OF NATURAL SCIENCE GYEONGSANG NATIONAL UNIVERSITY)
  • Published : 2007.04.30
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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.

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References

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