The split common fixed-point problem for demicontractive mappings. (English) Zbl 1219.90185

Moudafi, A.

Inverse Probl. 26, No. 5, Article ID 055007, 6 p. (2010).

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:

90C48	Programming in abstract spaces
90C25	Convex programming
68W10	Parallel algorithms in computer science
65K10	Numerical optimization and variational techniques
49J53	Set-valued and variational analysis
92C55	Biomedical imaging and signal processing

Keywords:

convex programming; parallel algorithms; optimization and variational techniques; set-valued and variational analysis; biomedical imaging and signal processing

Citations:

Zbl 1189.65111; Zbl 1126.47057; Zbl 1066.65047