FINDING COMMON FIXED POINTS OF A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS IN A BANACH SPACE

• AOYAMA KOJI

  Chiba University

• KIMURA YASUNORI

• TAKAHASHI WATARU

• TOYODA MASASHI

  Tamagawa University

Abstract

The main purpose of this paper is to study an iteration procedure for finding a common fixed point of a countable family of nonexpansive mappings in Banach spaces. We introduce a Mann type iteration procedure. Then we prove that such a sequence converges weakly to a common fixed point of a countable family of nonexpansive mappings. Moreover, we apply our result to the problem of finding a common fixed point of a pair of nonexpansive mappings and the problem of finding a common solution of the fixed point problem and the variational inequality problem.

Journal

• Scientiae Mathematicae Japonicae

  Scientiae Mathematicae Japonicae 66 (1), 89-99, 2007

  International Society for Mathematical Sciences

Keywords

• nonexpansive mappings
• weak convergence
• common fixed point

Details

• CRID: 1390565134833761024
• NII Article ID: 10019758613
• NII Book ID: AA1150654X
• DOI: 10.32219/isms.66.1_89
• ISSN: 13460447
• Text Lang: en
• Data Source:
  • JaLC
  • CiNii Articles
• Abstract License Flag: Disallowed