Multiple-Set Split Feasibility Problems forκ-Strictly Pseudononspreading Mapping in Hilbert Spaces

Abstract

The purpose of this paper is to prove some weak and strong convergence theorems for solving the multiple-set split feasibility problems forκ-strictly pseudononspreading mapping in infinite-dimensional Hilbert spaces by using the proposed iterative method. The main results presented in this paper extend and improve the corresponding results of Xu et al. (2006), of Osilike et al. (2011), and of many other authors.

A Strong Convergence Algorithm for the Two-Operator Split Common Fixed Point Problem in Hilbert Spaces

“…By Lemma 3, a resolvent of a maximal monotone operator is firmly nonexpansive. Hence, we may put = and = in (20) to get the conclusion which follows from Theorem 7.…”

“…The sequence { } generated by the algorithm converges weakly to a solution of SFP (5); compare [14][15][16]. Under the assumption that SFP (5) has a solution, there are many algorithms designed to approximate a solution of SFP; compare [16][17][18][19][20][21][22][23] and the references therein.…”

On the split equality common fixed point problem for quasi-nonexpansive multi-valued mappings in Banach spaces

“…In [10], Moudafi proposed an iteration scheme and obtained a weak convergence theorem of the split common fixed point problem for demicontractive mappings in the setting of two Hilbert spaces. Since then, the split common fixed point problems of other nonlinear mappings in the setting of two Hilbert spaces have been studied by some authors, see, for instance, [7,8,10,11,13,14,20].…”

On the split common fixed point problem for nonexpansive semigroups in Banach spaces

“…In [10], Moudafi proposed an iteration scheme and obtained a weak convergence theorem of the split common fixed point problem for demicontractive mappings in the setting of two Hilbert spaces. Since then, the split common fixed point problems of other nonlinear mappings in the setting of two Hilbert spaces have been studied by some authors, see, for instance, [2,[11][12][13][14]. In [15], Cholamjiak et al proved a strong convergence theorem for split feasibility problem involving a uniformly asymptotically regular nonexpansive semigroup and a total asymptotically strict pseudocontractive mapping in Hilbert spaces.…”