Convergence analysis for split hierachical monotone variational inclusion problem in Hilbert spaces

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 make our to be potentially more applicable than most existing methods literature. Under standard mild assumption monotonicity SHMVIP associated mappings, establish strong convergence algorithm.We present some applications main result approximate Convex Minimization (SHCMP) Inequality (SHVIP). Some numerical experiments are presented illustrate performance behavior method. The paper extends complements related results