A strong convergence theorem for total asymptotically pseudocontractive mappings in Hilbert spaces. (English) Zbl 1386.47007

Summary: A demiclosedness principle for total asymptotically pseudocontractive mappings in Hilbert spaces is established. The strong convergence to a fixed point of total asymptotically pseudocontraction in Hilbert spaces is obtained based on demiclosedness principle, metric projective operator, and hybrid iterative method. The main results presented in this paper extend and improve the corresponding results of H.-Y. Zhou [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 9, 3140–3145 (2009; Zbl 1207.47052)], X.-L. Qin et al. [Fixed Point Theory Appl. 2011, Article ID 859795, 11 p. (2011; Zbl 1215.47081)] and of many other authors.


47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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