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The split common fixed-point problem for demicontractive mappings. (English) Zbl 1219.90185
Summary: Based on the very recent work by Y. Censor and A. Segal [J. Convex Anal. 16, No. 2, 587–600 (2009; Zbl 1189.65111)] and inspired by H.-K. Xu [Inverse Probl. 22, No. 6, 2021–2034 (2006; Zbl 1126.47057)] and Q. Yang [Inverse Probl. 20, No. 4, 1261–1266 (2004; Zbl 1066.65047)]. we investigate an algorithm for solving the split common fixed-point problem for the class of demicontractive operators in a Hilbert space. Our results improve and/or develop previously discussed feasibility problems and related algorithms. It is worth mentioning that the convex feasibility formalism is at the core of the modeling of many inverse problems and has been used to model significant real-world problems, for instance, in sensor networks, in radiation therapy treatment planning, in computerized tomography and data compression.
MSC:
90C48Programming in abstract spaces
90C25Convex programming
68W10Parallel algorithms
65K10Optimization techniques (numerical methods)
49J53Set-valued and variational analysis
92C55Biomedical imaging and signal processing, tomography