A parallel monotone hybrid algorithm for a finite family of $$G-$$nonexpansive mappings in Hilbert spaces endowed with a graph applicable in signal recovery

A parallel method for common variational inclusion and common fixed point problems with applications

“…In the first part of the experiment, we investigate the behavior of our algorithm and then compare it with Algorithm 1 of Suantai et al [23] and Algorithm 2 of Suparatulatorn et al [24]. We select the signal size to be N = 4096 and M = 2048.…”

“…These constraints can be reformulated using a nonlinear functional model. We are motivated to study common variational inclusion and common fixed point problems in this paper because the problem can be utilized to solve real-world problems such as signal recovery and image recovery problems with various blurred filters, see [23,25]. We also show that our problem can be applied for solving signal recovery with various blurred filters as shown in Section 4.…”

“…where F i , S i are single valued mappings on H and G i : H → 2 H is a multivalued mapping for all i ∈ K. For finding a common fixed point of a finite family of G-nonexpansive mappings {S i } i∈K , Suantai et al [23] introduced Algorithm 1 in H with directed graphs. This algorithm is defined as follows:…”

A modified Mann algorithm for the general split problem of demicontractive operators

“…Algorithm 1.1 Initialization: Let x 0 ∈ H 1 be arbitrary and x n+1 be recursively dened by ). Some interesting studies of the SCFP and the associated problems can be found in [6,13,14,15]. Kangtunyakarn [8] recently presented the General Split Feasibility Problem (GSFP) in which its aim is to determine a point, x, satisfying…”

A Modified Inertial Parallel Viscosity-Type Algorithm for a Finite Family of Nonexpansive Mappings and Its Applications

“…Recently, there has been some research involving the parallel method for solving many problems. It is shown that the method can be applied in real-world problems such as image deblurring and related applications [15,16].…”