On semilocal convergence of three-step Kurchatov method under weak condition

Abstract The purpose of this paper to establish the semilocal convergence analysis three-step Kurchatov method under weaker conditions in Banach spaces. We construct recurrence relations assumption that involved first-order divided difference operators satisfy $$\omega $$ ω condition. Theorems are given for existence-uniqueness balls enclosing unique solution. application iterative is shown by solving nonlinear system equations and Hammerstein-type integral equations. It illustrates theoretical development study.