LAUSR

Inspired by the works of Alvarez and Attouch (Set-Valued Anal. 9:3–11, 2001), López et al. (Inverse Probl. 28:ID085004, 2012), Takahashi (Arch. Math. (Basel) 104(4):357–365, 2015) and Suantai et al. (Appl. Gen. Topol. 18(2):345–360, 2017), as well as Promluang and Kuman (J. Inform. Math. Sci. 9(1):27–44, 2017), we 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.