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

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Abstract

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).

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Authors and Affiliations

  1. Department of Mathematics, Yibin University, Yibin, 644007, Sichuan Province, P. R. China

    Shi-sheng Zhang  (张石生)

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, P. R. China

    Joseph H. W. Lee  (李向荣) & Chi Kin Chan  (陈志坚)

Authors
  1. Shi-sheng Zhang  (张石生)
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  2. Joseph H. W. Lee  (李向荣)
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  3. Chi Kin Chan  (陈志坚)
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Corresponding author

Correspondence to Shi-sheng Zhang  (张石生).

Additional information

Contributed by ZHANG Shi-sheng

Project supported by the Natural Science Foundation of Yibin University of China (No. 2007-Z003)

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Zhang, Ss., Lee, J.H.W. & Chan, C.K. Algorithms of common solutions to quasi variational inclusion and fixed point problems. Appl. Math. Mech.-Engl. Ed. 29, 571–581 (2008). https://doi.org/10.1007/s10483-008-0502-y

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  • DOI: https://doi.org/10.1007/s10483-008-0502-y

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2000 Mathematics Subject Classification

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