Split Common Fixed Point Problem of Nonexpansive Semigroup

The split common fixed point problem of two infinite families of demicontractive mappings and the split common null point problem

“…As application, we obtain strong convergence theorems for split monotone variational inclusion and split variational inequality problems. Our results improve and extend some recent results due to Cui and Wang [9], Takahashi [21], Tang and Liu [22], Moudafi [15], as well as Eslamian and Vahidi [17].…”

“…where α n ∈ (δ, 1 − δ) for a small enough δ > 0, β ∈ (0, 1) and γ ∈ 0, 1 λβ with λ being the spectral radius of the operator A * A. In [17], Eslamian and Vahidi studied an algorithm for solving the split common fixed point problem for an infinite family of quasi-nonexpansive mappings. They established the following theorem.…”

“…Theorem 1.1. [17] Let H 1 and H 2 be two real Hilbert spaces, and A : H 1 −→ H 2 be a bounded linear operator. Let S i : H 1 −→ H 1 and T i : H 2 −→ H 2 , (i ∈ N), be two infinite families of quasi-nonexpansive mappings such that S i − I and T i − I are demiclosed at 0.…”

Split equality monotone variational inclusions and fixed point problem of set-valued operator

“…Initiated by SFP, several split type problems have been investigated and studied, for example, the split common fixed point problem (SCFP) [5], the split variational inequality problem (SVIP) [6], and the split null point problem (SCNP) [7]. Many authors have studied the SFP in infinite-dimensional Hilbert spaces, see, for example, [8][9][10][11][12][13] and some of the references therein. Many nonlinear problems arising in applied areas such as image recovery, signal processing, and machine learning are mathematically modeled as a nonlinear operator equation and this operator is decomposed as the sum of two nonlinear operators, see [14][15][16][17].…”

Inertial method for split null point problems with pseudomonotone variational inequality problems

“…Recently, Eslamain and Vahidi [18] considered the problem of finding a common solution of the split null point problem and fixed point for maximal monotone operators. Later, Jailoka and Suantai [23] presented an algorithm for studying the split common fixed point and null problem for demicontractive operators and maximal monotone operators and proved a strong convergence theorem.…”