Strong convergence of a generalized forward–backward splitting method in reflexive Banach spaces

Perturbed Halpern-type Algorithm Involving Multiple Split Equality Problems With Application to Dynamical Systems

“…The iterative scheme does not require prior knowledge of operator norm, we give some applications of split equality problem to dynamical systems. Furthermore our method of proof is of independent interest, as it does not involve the use of cases as done in all the three motivating results above (i.e [1], [13] and [24]).…”

“…In 2020, T. M. Tuyen et al [24] introduced and study the following algorithm in reflexive real Banach space:…”

“…, provided that some conditions on Ω, the parameters sequences {β i } N i=1 , {α n } are satisfied (see [24]). In 2020 Ali et al studied a new mapping called demi − generalized mapping, they obtained some properties of the new mapping and constructed the following iterative algorithm {x n } defined as follows:…”

“…, n ≥ 1, Under some conditions on the control sequences, the authors proved that the sequence {x n } converges strongly to P f Ω x. Motivated by [13], [24] and [1], in this paper, we study split equality problem involving the common solution for a finite family of split equality problems, demigeneralized mappings, monotone inclusion problems in a p-uniformly convex, uniformly smooth real Banach space. Strong convergence theorem of the proposed method is obtained under standard and mild conditions.…”

A modified parallel monotone hybrid algorithm for a finite family of $\mathcal{G}$-nonexpansive mappings apply to a novel signal recovery

“…Many mathematicians have used this algorithm (5) to modify in many ways such as the proximal point algorithm [13,21,25,28] and the gradient method [11,30,41,42]. For its applications, there have been modifications of the algorithm (5) in many various areas of science and physic etc., (see [7,8,10,16,17,23,26,44,36]).…”