Applied Mathematics and Mechanics

, Volume 29, Issue 5, pp 571–581 | Cite as

Algorithms of common solutions to quasi variational inclusion and fixed point problems

  • Shi-sheng Zhang (张石生)Email author
  • Joseph H. W. Lee (李向荣)
  • Chi Kin Chan (陈志坚)


The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space. Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich (Ekonomika i Matematicheskie Metody, 1976, 12(4):747–756), but also extend and replenish the corresponding results obtained by Iiduka and Takahashi (Nonlinear Anal TMA, 2005, 61(3):341–350), Takahashi and Toyoda (J Optim Theory Appl, 2003, 118(2):417–428), Nadezhkina and Takahashi (J Optim Theory Appl, 2006, 128(1):191–201), and Zeng and Yao (Taiwanese Journal of Mathematics, 2006, 10(5):1293–1303).

Key words

variational inclusion multi-valued maximal monotone mapping inversestrongly monotone mapping metric projection fixed point nonexpansive mapping 

Chinese Library Classification


2000 Mathematics Subject Classification

47H09 47H05 47J05 47J25 


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Copyright information

© Shanghai University and Springer-Verlag GmbH 2008

Authors and Affiliations

  • Shi-sheng Zhang (张石生)
    • 1
    Email author
  • Joseph H. W. Lee (李向荣)
    • 2
  • Chi Kin Chan (陈志坚)
    • 2
  1. 1.Department of MathematicsYibin UniversityYibinP. R. China
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHung Hom, Kowloon, Hong KongP. R. China

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