New inertial algorithm for solving split common null point problem in Banach spaces

Abstract

Inspired by the works of Alvarez propose a new inertial algorithm for solving split common null point problem without the prior knowledge of the operator norms in Banach spaces. Under mild and standard conditions, the weak and strong convergence theorems of the proposed algorithms are obtained. Also the split minimization problem is considered as the application of our results. Finally, the performances and computational examples are presented, and a comparison with related algorithms is provided to illustrate the efficiency and applicability of our new algorithm. MSC: 47H05; 47H09; 49J53; 65J15; 90C25

On the convergence and applications of the inertial-like method for null-point problems

“…We have included several numerical examples which show the efficiency and reliability of Algorithm 3.1 and Algorithm 3.2. We have also made comparisons of Algorithm 3.1 and Algorithm 3.2 with other four algorithms in Sitthithakerngkiet et al [27], Kazimi and Riviz [12], Tang [28], Dadashi and Postolach [8] confirming some advantages of our novel inertial algorithms.…”

“…where A = B 1 and B = T * (I − J λ B 2 )T with γ− cocoercive, γ = 1 T * T . In addition to showing the behavior of our algorithms, the results of Sitthithakerngkiet et al [27], Kazimi and Riviz [12] without inertial process and Tang [28] with general inertial method are compared. For the experiment setting, we choose the following parameters: T ∈ R m * n is generated randomly with m = 2 6 , 2 7 , n = 2 8 , 2 9 , x 0 ∈ R n is K-spikes (K = 40, 60) with amplitude ±1 distributed in whole domain randomly.…”

“…More works on inertial methods, one can refer Dang et al [9], Moudafi et al [18], Suantai et al [26], Tang [28], and therein. Theoretically, the condition (1.10) on the parameter α n is too strict for the convergence of the inertial algorithm.…”

“…The comparisons of Algorithm 3.1, Algorithm 3.2, Sitthithakerngkiet et al[27], Kazmi et al[12], Tang[28] …”

Simple inertial methods for solving split variational inclusions in Banach spaces

“…Lemma (Tang 37 ) Let H be a real Hilbert space, E be a strictly convex reflexive and smooth Banach space and J be the normalized duality mapping on E . Let B 1 : H → 2 H and be maximal operators such that and , respectively.…”