An iterative method for amenable semigroup and infinite family of non expansive mappings in Hilbert spaces

Document Type: Research Paper

Authors

1 Department of Mathematics, Bonab Higher Education Complex

2 Faculty of Mathematical Sciences University of Tabriz, Tabriz, Iran

Abstract

begin{abstract}
In this paper, we introduce an iterative method for amenable
semigroup of non expansive mappings and infinite family of non
expansive mappings in the frame work of Hilbert spaces. We prove the
strong convergence of the proposed iterative algorithm to the unique
solution of a variational inequality, which is the optimality
condition for a minimization problem. The results presented in this
paper mainly extend the corresponding results announced by Qin et
al. [X. Qin, Y. J. Cho, and S. M. Kang, An iterative method for an
infinite family of non-expansive mappings in Hilbert spaces, Bull.
Malays. Math. Sci. Soc. 32 (2009) 161-171] and many others.

end{abstract}

Keywords



Volume 38, Issue 2
July and August 2012
Pages 369-389
  • Receive Date: 25 February 2011
  • Revise Date: 13 December 2010
  • Accept Date: 13 December 2010