Strong convergence theorems of a new hybrid projection method for finite family of two hemi-relatively nonexpansive mappings in a Banach space

Volume 92 / 2011

Kriengsak Wattanawitoon, Poom Kumam Banach Center Publications 92 (2011), 379-390 MSC: Primary 47H10; Secondary 47H09. DOI: 10.4064/bc92-0-26

Abstract

In this paper, we prove strong convergence theorems of the hybrid projection algorithms for finite family of two hemi-relatively nonexpansive mappings in a Banach space. Using this result, we also discuss the resolvents of two maximal monotone operators in a Banach space. Our results modify and improve the recently ones announced by Plubtieng and Ungchittrakool [Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space, J. Approx. Theory 149 (2007), 103–115], Matsushita and Takahashi [A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory 134 (2005), 257–266] and many others.

Authors

  • Kriengsak WattanawitoonDepartment of Mathematics and Statistics
    Faculty of Science and Agricultural Technology
    Rajamangala University of Technology Lanna Tak
    Tak 63000, Thailand
    e-mail
  • Poom KumamDepartment of Mathematics, Faculty of Science
    King Mongkut's University of Technology Thonburi (KMUTT)
    Bangmod, Thrungkru, Bangkok 10140, Thailand
    e-mail

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