Abstract

We first introduce a broad semigroup of not necessarily continuous mappings in a Banach space which contains discrete semigroups generated by generalized nonspreading mappings and semigroups of φ-nonexpansive mappings. Then we establish a weak convergence theorem of Mann's type iteration for the semigroups of mappings in a Banach space. Using the result, we obtain well-known and new theorems which are connected with weak convergence results in Banach spaces.

Author information

Contact details are reproduced from the original publication and may be historical.

Saud M. Alsulami

Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

alsulami@kau.edu.sa

Nawab Hussain

Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

nhusain@kau.edu.sa

Wataru Takahashi

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan

wataru@is.titech.ac.jp

Keywords

  • Attractive point
  • Banach space
  • fixed point
  • generalized nonspreading mapping
  • invariant mean
  • weak converegence
  • nonexpansive semigroup
  • strongly asymptotically invariant net

Mathematics Subject Classification

47H05, 47H09, 47H20

Suggested citation

S. M. Alsulami, N. Hussain, W. Takahashi. “Weak Convergence Theorems for Semigroups of Not Necessarily Continuous Mappings in Banach Spaces.” Journal of Convex Analysis 22 (2015), No. 1, 81–100.

Copyright Heldermann Verlag 2015