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Strong convergence of monotone CQ algorithm for relatively nonexpansive mappings. (English) Zbl 1169.47056
This paper extends and improves the results of X.–L. Qin and Y.–F. Su [Nonlinear Anal., Theory Methods Appl. 67, No. 6 (A), 1958–1965 (2007; Zbl 1124.47046)]. The extension and improvement are in two notable directions. (i) The authors employ the monotone CQ method to modify the CQ method of Qin and Su. (ii) The authors relax the restriction on T:CC from uniformly continuous to continuous. Their monotone CQ method does not require the Kadec–Klee property, the demiclosedness principle, Opial’s condition, or other weak topological technologies.
MSC:
47J25Iterative procedures (nonlinear operator equations)
47H05Monotone operators (with respect to duality) and generalizations
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces