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Iterative methods for the class of quasi-contractive type operators and comparison of their rate of convergence in convex metric spaces. (English) Zbl 1462.54058
Summary: We introduce modified Noor iterative method in a convex metric space and apply it to approximate fixed points of quasi-contractive operators introduced by V. Berinde [Demonstr. Math. 38, No. 1, 177–184 (2005; Zbl 1074.47030)]. Our results generalize and improve upon, among others, the corresponding results of Berinde [loc. cit.], A. O. Bosede [Bull. Math. Anal. Appl. 3, No. 4, 140–145 (2011; Zbl 1314.47101)] and W. Phuengrattana and S. Suantai [Thai J. Math. 11, No. 1, 217–226 (2013; Zbl 1294.47090)]. We also compare the rate of convergence of proposed iterative method to the iterative methods due to Noor, Ishikawa and Mann. It has been observed that the proposed method is faster than the other three methods. Incidently the results obtained herein provide analogues of the corresponding results of normed spaces and holds in \(CAT(0)\) spaces, simultaneously

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
47J26 Fixed-point iterations
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