Convergence Criteria of a Three-Step Scheme under the Generalized Lipschitz Condition in Banach Spaces

In the given study, we investigate three-step NTS’s ball convergence for solving nonlinear operator equations with a order of five in Banach setting. A operator’s first-order derivative is assumed to meet generalized Lipschitz condition, also known as κ-average condition. Furthermore, several theorems on same method spaces are developed conditions that operators must satisfy radius or center-Lipschitz condition weak and κ positive integrable but not necessarily non-decreasing function. This novel approach allows more precise analysis even without requirement new circumstances. As result, broaden applicability iterative approaches. The theoretical results supported further by illuminating examples. theorem investigates location solution ϵ* existence it. end, achieve weaker sufficient criteria specific knowledge position than previous efforts requiring computational effort. We obtain well some applying functions κ(u). Numerical tests carried out corroborate hypotheses established this work.