On the strong convergence of an algorithm about firmly pseudo-demicontractive mappings for the split common fixed-point problem. (English) Zbl 1318.47101

Summary: Based on the recent work by Y. Censor and A. Segal [J. Convex Anal. 16, No. 2, 587–600 (2009; Zbl 1189.65111)] and inspired by A. Moudafi [Inverse Probl. 26, No. 5, Article ID 055007, 6 p. (2010; Zbl 1219.90185)], we modify the algorithm of demicontractive operators proposed by Moudafi and study the modified algorithm for the class of firmly pseudodemicontractive operators to solve the split common fixed-point problem in a Hilbert space. We also give a strong convergence theorem under some appropriate conditions. Our work improves and/or develops the work of Moudafi, Censor and Segal, and other results.


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