The regularity properties of a family of closed convex sets with nonempty intersection are investigated in the frame of a real Hilbert space. The significant role of these properties in solving convex feasibility problems with projection algorithms is pointed out.
On the Mann-type iteration and the convex feasibility problem
✍ Scribed by Ştefan Măruşter; Cristina Popirlan
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 158 KB
- Volume
- 212
- Category
- Article
- ISSN
- 0377-0427
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✦ Synopsis
The weak and strong convergence of a sequence generated by a Mann-type iteration are investigated in the frame of a real Hilbert space. Some applications to the projection method for the convex feasibility problem are given.
📜 SIMILAR VOLUMES
The purpose of this note is to study the estimation of errors of the Mann iterative process with random errors. It is shown that the accumulative errors in iterative process is bounded and the errors is controllable with some conditions.
114᎐125 converge strongly to the solution of the equation Tx s f. Furthermore, if E is a uniformly smooth Banach space and T : E ª E is demicontinuous and strongly accretive, it is also proved that both the Ishikawa and the Mann iteration methods with errors converge strongly to the solution of the
The pu~'pose of this paper is to introduce and study the existence of solutions and convergence of Mann and Ishikawa iterative processes for a class of variational inclusions with accretive type mappings in Banach spaces. The results presented in this paper extend and improve the corresponding resul