Block-iterative algorithms for solving convex feasibility problems in Hilbert and in Banach spaces

Abstract

We establish convergence theorems for two different block-iterative methods for solving the problem of finding a point in the intersection of the fixed point sets of a finite number of nonexpansive mappings in Hilbert and in finite-dimensional Banach spaces, respectively.

Strong and weak convergence theorems for a new split feasibility problem

“…Since convex feasibility problems and split feasibility problems can be widely applied in many areas, some researchers are attracted in constructing some algorithms to solve split feasibility problem, see for instance [6][7][8][9].…”

Strong convergence theorem of two-step iterative algorithm for split feasibility problems

“…1 Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China. 2 College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China.…”

Hybrid Projection Algorithm for Two Countable Families of Hemirelatively Nonexpansive Mappings and Applications

“…There is a considerable investigation on (CFP) in the framework of Hilbert spaces which captures applications in various disciplines such as image restoration [50][51][52][53], computer tomography [54], and radiation therapy treatment planning [55]. In computer tomography with limited data, in which an unknown image has to be reconstructed from a priori knowledge and from measured results, each piece of information gives a constraint which in turn gives rise to a convex set to which the unknown image should belong (see [56]). …”