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Received June 27, 2020; Accepted April 10, 2021; Published May 15, 2021
Abstract. In this paper, we introduce the concept of a generalized convex metric space as a generalization of a convex metric space, which is due to Takahashi [A convexity in metric space and nonexpansive mappings, Kodai Math. Seminar Reports 22 (1970), 142-149], and give the iterative scheme due to Xiao, Sun and Huang [Approximating common fixed points of asymptotically quasi-nonexpansive mappings by a k+1-step iterative scheme with error terms, J. Comput. Appl. Math. 233 (2010), 2062-2070]. We also establish strong convergence of this scheme to a unique common fixed point of a finite family of asymptotically quasi-nonexpansive mappings. Our results generalize/extend several existing results.
How to Cite this Article:
M.A. Ahmed, Ismat Beg, S. A. Khafagy, H.A. Nafadi, Convergence of a k+1-step iterative scheme with errors for asymptotically quasi-nonexpansive mappings in generalized convex metric spaces, Communications in Optimizatoin Theory, Vol. 2021 (20201), Article ID 5, pp. 1-9.