Journal of Applied Mathematics
Volume 2012 (2012), Article ID 435676, 15 pages
http://dx.doi.org/10.1155/2012/435676
Research Article

Cyclic Iterative Method for Strictly Pseudononspreading in Hilbert Space

Bin-Chao Deng, Tong Chen, and Zhi-Fang Li

School of Management, Tianjin University, Tianjin 300072, China

Received 17 April 2012; Revised 1 June 2012; Accepted 1 June 2012

Academic Editor: Hong-Kun Xu

Copyright © 2012 Bin-Chao Deng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let { 𝑇 𝑖 } 𝑁 𝑖 = 1 be 𝑁 strictly pseudononspreading mappings defined on closed convex subset 𝐶 of a real Hilbert space 𝐻 . Consider the problem of finding a common fixed point of these mappings and introduce cyclic algorithms based on general viscosity iteration method for solving this problem. We will prove the strong convergence of these cyclic algorithm. Moreover, the common fixed point is the solution of the variational inequality ⟨ ( 𝛾 𝑓 − 𝜇 𝐵 ) 𝑥 ∗ , 𝑣 − 𝑥 ∗ ⋂ ⟩ ≤ 0 , ∀ 𝑣 ∈ 𝑁 𝑖 = 1 𝐹 𝑖 𝑥 ( 𝑇 𝑖 ) .