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Modified block iterative method for solving convex feasibility problem, equilibrium problems and variational inequality problems

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Abstract

The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-ϕ-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem (CFP) and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.

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Authors and Affiliations

  1. College of Statistics and Mathematics, Yunnan Uniersity of Finance and Economics, Kunming, 650221, P. R. China

    Shi Sheng Zhang

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

    Chi Kin Chan & H. W. Joseph Lee

Authors
  1. Shi Sheng Zhang
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  2. Chi Kin Chan
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  3. H. W. Joseph Lee
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Correspondence to Shi Sheng Zhang.

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Supported by Natural Science Foundation of Yibin University (Z-2009, No. 3)

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Zhang, S.S., Chan, C.K. & Joseph Lee, H.W. Modified block iterative method for solving convex feasibility problem, equilibrium problems and variational inequality problems. Acta. Math. Sin.-English Ser. 28, 741–758 (2012). https://doi.org/10.1007/s10114-011-0099-3

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  • DOI: https://doi.org/10.1007/s10114-011-0099-3

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