@article{Regmi_Argyros_George_Argyros_2023, title={Extended Semilocal Convergence for Chebyshev-Halley-Type Schemes for Solving Nonlinear Equations under Weak Conditions}, volume={4}, url={https://ojs.wiserpub.com/index.php/CM/article/view/2070}, DOI={10.37256/cm.4120232070}, abstractNote={<p>The application of the Chebyshev-Halley type scheme for nonlinear equations is extended with no additional conditions. In particular, the purpose of this study is two folds. The proof of the semi-local convergence analysis is based on the recurrence relation technique in the first fold. In the second fold, the proof relies on majorizing sequences. Iterates are shown to belong to a larger domain resulting in tighter Lipschitz constants and a finer convergence analysis than in earlier works. The convergence order of these methods is at least three. The numerical example further validates the theoretical results.</p>}, number={1}, journal={Contemporary Mathematics}, author={Regmi, Samundra and Argyros, Ioannis K. and George, Santhosh and Argyros, Christopher I.}, year={2023}, month={Jan.}, pages={1–16} }