Abstract In this paper, we study the problem of finding solution system monotone variational inclusion problems recently introduced by Chang et al. (Optimization 70(12):2511–2525, 2020) with constraint a fixed-point set quasipseudocontractive mappings. We propose new iterative method that employs an inertial technique self-adaptive step size for approximating in Hilbert spaces and prove strong-...

Abstract In this paper, we introduce a new iterative algorithm for approximating common solution of Split Hierarchical Monotone Variational Inclusion Problem (SHMVIP) and Fixed Point (FPP) k-strictly pseudocontractive mappings in real Hilbert spaces. Our proposed method converges strongly, does not require the estimation operator norm it is without imposing strict condition compactness; these m...

In this paper, the split fixed point and variational inclusion problem is considered. With help of technique, Tseng-type splitting method self-adaptive rule, an iterative algorithm proposed for solving in which involved operators S T are demicontractive g plain monotone. Strong convergence theorem proved under some mild conditions.

<p style='text-indent:20px;'>A new strong convergence iterative method for solving a split variational inclusion problem involving bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an scheme comprised of inertial extrapolation step together with the Mann-type step. A theorem iterates generated by given under suitable conditions. I...