A common solution of finite family of a new class of split monotone variational inclusion problems

Abstract

Based on the recent important results of Moudafi [Journal of Optimization Theory and Applications 150(2011), 275-283], Tian and Jiang [Journal of Inequalities and Applications (2017)] and other related results on variational problems, we study a new class of split monotone inclusion problems in Hilbert spaces. As part of our main results, we introduce a new iterative algorithm for approximating a common solution of finite family of the new class of split monotone variational inclusion problems. The sequence of the algorithm is proved to converge strongly in the setting of Hilbert spaces. As application, we solved finite family of split convex minimization problems. Our results extend and improve the results of Censor et al. [21], Moudafi [38], Tian and Jiang [45], and a host of other important results in this direction.