A strongly convergent algorithm for the split common fixed point problem

Weak Convergence Theorems on the Split Common Fixed Point Problem for Demicontractive Continuous Mappings

“…Subsequently, this result was extended to quasi-nonexpansive operators [7], demicontractive operators [8,9], two groups of finitely many firmly quasi-nonexpansive mappings [10,11], and the more general common null point problem [12]. Also, some variants of method (2) have been considered in [13][14][15][16].…”

A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing

“…Remark 4. Figures 2-5 show that the sequence {β n } improves the convergence profile of [14,15]. Our algorithm (Algorithm 5) converges faster than Cui and Wang's algorithm and Boikanyo's algorithm.…”

“…In 2015, Boikanyo [15] extended Cui and Wang's results and proposed the following Algorithm 2 for demicontrative operators U and T with U λ := (1 − λ)I + λU for any λ ∈ (0, 1 − κ), which converges strongly to a solution of the problem (6) when a solution exists: For any u ∈ H,…”

“…In this paper, motivated by Boikanyo's algorithm [15] and the algorithm of Huimin et al [16], we will propose the following Algorithm 4 for demicontrative operators U and T with U λ n := (1 − λ n )I + λ n U for any λ n ∈ (0, 1 − κ):…”

“…Let A be the random matrix (k × N) such that each entire is in [0, 1]. Let y = Ax * be such that x * 1 ≤ t. Set up the problem (15). We choose λ = 1 2 , α = 1 n , β = 1 n 2 , u = 1 · · · 1 † , f (x) = (x − p)/4 + p and initial x 1 randomly be such that p 1 , x 1 1 ≤ t. Thus C = {x ∈ R N : x 1 ≤ t}.…”