WEAK CONVERGENCE THEOREMS FOR FINDING COMMON ELEMENTS OF FINITE SETS IN BANACH SPACES

• IBARAKI TAKANORI

  Nagoya University

• TAKAHASHI WATARU

Abstract

In this paper, we deal with the problem for finding a common element of finite sets in a Banach space. We first prove that an operator given by a convex combination of sunny generalized nonexpansive retractions in a Banach space is asymptotically regular. Using this result, we obtain a weak convergence theorem which is connected with the problem of image recovery. Further, using another weak convergence theorem, we prove a weak convergence theorem of Mann’s type for finding a common element of finite sets in a Banach space.

Journal

• Scientiae Mathematicae Japonicae

  Scientiae Mathematicae Japonicae 66 (3), 303-312, 2007

  International Society for Mathematical Sciences

Keywords

• Generalized nonexpansive mapping
• sunny generalized nonexpansive retract
• image recovery
• the feasibility problem
• Banach space

Details

• CRID: 1390846609810325632
• NII Article ID: 10019780342
• NII Book ID: AA1150654X
• DOI: 10.32219/isms.66.3_303
• ISSN: 13460447
• Text Lang: en
• Data Source:
  • JaLC
  • CiNii Articles
• Abstract License Flag: Disallowed