A new iterative method for common fixed points of a finite family of nonexpansive mappings

• Main Authors: Imnang S., Suantai S.
• Format: Article
• Language: English
• Published: 2014
• Online Access: http://www.scopus.com/inward/record.url?eid=2-s2.0-68349083653&partnerID=40&md5=d8d0a508373069cfd6a35c23b9223c5e; http://cmuir.cmu.ac.th/handle/6653943832/5832
• Institution: Chiang Mai University

Let X be a real uniformly convex Banach space and C a closed convex nonempty subset of X. Let {Ti}i=1r be a finite family of nonexpansive self-mappings of C. For a given x1 ∈ C, let {xn} and {xn(i)}, i = 1,2,.., r, be sequences defined xn(0) = xn, xn(i) = an1(1)T1xn(0) + (1 - an1(1)xn(0), xn(2) = an2(2) T2xn(1) + an1(2) T1xn + (1 - an2(2) - an1(2))xn,..;, xn+1 = xn(r) - anr(r) Trxn(r-1) + an(r-1)(r) Tr-1xn(r-2) +..; + an1(r)T1xn + (1 - an(r)(r) - an(r-1)(r) -..; - an1(r)xn, n ≥ 1, where ani(j) ∈ (0, 1) for all j ∈ {1, 2,..,r}, n ∈ N and i = 1, 2,..;, j. In this paper, weak and strong convergence theorems of the sequence {xn} to a common fixed point of a finite family of nonexpansive mappings Ti (i = 1, 2,..;, r) are established under some certain control conditions.