On δ-convergence of the Ishikawa iterative process for nonexpansive mappings in cat(0) spaces

• Main Authors: Laokul,T., Panyanak,B.
• Format: Article
• Published: Yokohama Publishers 2015
• Subjects: Geometry and Topology; Control and Optimization; Applied Mathematics; Analysis
• Online Access: http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84894127839&origin=inward; http://cmuir.cmu.ac.th/handle/6653943832/38714
• Institution: Chiang Mai University

Let C be a nonempty closed convex subset of a complete CAT(0) space and T: C → C be a nonexpansive mapping with a fixed point. Suppose that {xn} is defined by x1 ∈ C and xn+1 = tnT[snTxn ⊕ (1-sn)xn] ⊕ (1-tn)xn for all n ≥ 1, where {tn} and {sn} are sequences in [0, 1] such that one of the following two conditions is satisfied: (i)∑∞ n=1 tn (1-tn) = ∞ and lim suptn stn < 1; (ii)∑∞ n=1 tn sn = ∞ and lim supn sn ≤ 1: Then the sequence {xn} δ-converges to a fixed point of T: This is an analog of a result in Banach spaces of Suzuki and Takahashi [29] and generalizes some results in [10] and [22]. © 2010 yokohama publishers.