Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h,η)-PROXIMAL MAPPING

  • Liu, Zeqing (Department of Mathematics Liaoning Normal University) ;
  • Chen, Zhengsheng (School of Management Dalian University of Technology) ;
  • Shim, Soo-Hak (The Research Institute of Natural Science Gyeongsang National University) ;
  • Kang, Shin-Min (Department of Mathematics and The Research Institute of Natural Science Gyeongsang National University)
  • Published : 2008.09.30
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Abstract

In this paper, a new class of $(h,{\eta})$-proximal for proper functionals in Hilbert spaces is introduced. The existence and Lip-schitz continuity of the $(h,{\eta})$-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.

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References

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