An iterative algorithm by viscosity approximation method for mixed equilibrium problems, variational inclusion and fixed point of an infinite family of pseudo-contractive mappings

Volume 92 / 2011

Phayap Katchang, Poom Kumam Banach Center Publications 92 (2011), 177-196 MSC: Primary 46C05, 47D03, 47H09, 47H10, 47H20. DOI: 10.4064/bc92-0-12

Abstract

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusion problems for inverse strongly monotone mappings and the set of common fixed points for an infinite family of strictly pseudo-contractive mappings in the setting of Hilbert spaces. We prove the strong convergence theorem by using the viscosity approximation method for finding the common element of the above four sets. Our results improve and extend the corresponding results of Peng and Yao [Math. Comput. Modelling 49 (2009), 1816–1828], Plubtieng and Sriprad [Fixed Point Theory Appl. 2009, Article ID 567147] and some well-known results in the literature.

Authors

  • Phayap KatchangDepartment of Mathematics
    Faculty of Science
    King Mongkut's University of Technology Thonburi (KMUTT)
    Bangmod
    Bangkok 10140, Thailand
    e-mail
  • Poom KumamDepartment of Mathematics
    Faculty of Science
    King Mongkut's University of Technology Thonburi (KMUTT)
    Bangmod
    Bangkok 10140, Thailand
    and
    Centre of Excellence in Mathematics, CHE
    Si Ayutthaya Rd.
    Bangkok 10400, Thailand
    e-mail

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