WEAK AND STRONG CONVERGENCE THEOREMS FOR NONEXPANSIVE SEMIGROUPS IN A BANACH SPACE SATISFYING OPIAL’S CONDITION

• ATSUSHIBA SACHIKO

• TAKAHASHI WATARU

Abstract

In this paper, we study the weak convergence of Mann’s type iteration procedure and the existence of nonexpansive retractions for commutative semigroups in Banach spaces which satisfy Opial’s condition. Further, we introduce an implicit iteration procedure for nonexpansive semigroups and then prove a strong convergence theorem for the nonexpansive semigroups in general Banach spaces.

Journal

• Scientiae Mathematicae Japonicae

  Scientiae Mathematicae Japonicae 65 (2), 147-160, 2007

  International Society for Mathematical Sciences

Keywords

• Fixed point
• nonexpansive mapping
• nonexpansive semigroup
• iteration
• weak convergence
• strong convergence

Details

• CRID: 1390283659856948736
• NII Article ID: 10019758872
• NII Book ID: AA1150654X
• DOI: 10.32219/isms.65.2_147
• ISSN: 13460447
• Text Lang: en
• Data Source:
  • JaLC
  • CiNii Articles
• Abstract License Flag: Disallowed