Ball convergence for combined three-step methods under generalized conditions in Banach space

Ioannis K. Argyros, Ramandeep Behl, Daniel Gonzalez, Sandile S. Motsa, Cameron University, Department of Mathematics Sciences, Lawton, OK 73505, USA e-mail: ioannisa@cameron.edu", "Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia e-mail: ramanbehl87@yahoo.in", "Universidad de Las Americas, Escuela de Ciencias Fisicas y Matematicas, Quito, 170125, Ecuador e-mail: daniel.gonzalez.sanchez@udla.edu.ec", "University of KwaZulu-Natal, School of Mathematics, Statistics and Computer Sciences, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa e-mail: sandilemotsa@gmail.com"
2020 Studia Universitatis Babes-Bolyai Matematica  
We give a local convergence analysis for an eighth-order convergent method in order to approximate a locally unique solution of nonlinear equation for Banach space valued operators. In contrast to the earlier studies using hypotheses up to the seventh Fréchet-derivative, we only use hypotheses on the first-order Fréchet-derivative and Lipschitz constants. Therefore, we not only expand the applicability of these methods but also provide the computable radius of convergence of these methods.
more » ... ly, numerical examples show that our results apply to solve those nonlinear equations but earlier results cannot be used. (2010) : 65G99, 65H10, 47J25, 47J05, 65D10, 65D99. Mathematics Subject Classification
doi:10.24193/subbmath.2020.1.10 fatcat:m73uwcloxra2vhtt6wp2xng2dm