Document Type : Research Paper
Department of Mathematics, Bonab Higher Education Complex
Faculty of Mathematical Sciences University of Tabriz, Tabriz, Iran
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.