Convergence Criteria of Three Step Schemes for Solving Equations

Samundra Regmi, Christopher I. Argyros, Ioannis K. Argyros, Santhosh George
2021 Mathematics  
We develop a unified convergence analysis of three-step iterative schemes for solving nonlinear Banach space valued equations. The local convergence order has been shown before to be five on the finite dimensional Euclidean space assuming Taylor expansions and the existence of the sixth derivative not on these schemes. So, the usage of them is restricted six or higher differentiable mappings. But in our paper only the first Frèchet derivative is utilized to show convergence. Consequently, the
more » ... heme is expanded. Numerical applications are also given to test convergence.
doi:10.3390/math9233106 fatcat:eo7dnglcpnfshh3troeibdjm6u