Multiple‐Set Split Feasibility Problems for Asymptotically Strict Pseudocontractions

Abstract

In this paper, we introduce an iterative method for solving the multiple-set split feasibility problems for asymptotically strict pseudocontractions in infinite-dimensional Hilbert spaces, and, by using the proposed iterative method, we improve and extend some recent results given by some authors.

Split equality problem for κ-asymptotically strictly pseudo-nonspreading mapping in Hilbert space

“…(iii) κ-asymptotically strictly pseudo-contraction [5], if there exists a constant κ ∈ [0, 1) and a sequence k n 1 and lim n→∞ k n = 1 such that…”

The Split Feasibility Problems for Countable Families of Asymptotically Strict Pseudocontractions

“…and proved that { } converges weakly to a split common fixed point * ∈ Γ, where : 1 → 1 and : 2 → 2 are two quasinonexpansive mappings, : 1 → 2 is a bounded linear operator, and * denotes the adjoint of . Motivated and inspired by the studies of Moudafi [10,11] and Chang et al [12], in this paper, we introduce an algorithm for solving the split feasibility problems for countable families of asymptotically strict pseudocontractions and prove some strong and weak convergence theorems for such mappings in Hilbert spaces. The results extend those of the authors [12] whose related research studies are restricted to the situation of at most finite families of such mappings.…”

Feasible iterative algorithms and strong convergence theorems for bi-level fixed point problems

“…It has been found that the (SFP) can also be used in various disciplines such as image restoration, computer tomograph and radiation therapy treatment planning [4,6,7]. The (SFP) in an infinite dimensional real Hilbert space can be found in [3,6,11,15,27,28,29].…”