On the local convergence of modified Homeier-like method in banach spaces
B. Panday1, J.P. Jaiswal2
1Regional Institute of Education, Bhopal, M.P. India-462013
2Maulana Azad National Institute of Technology, Bhopal, M.P. India-462003
Keywords: банахово пространство, локальная сходимость, нелинейное уравнение, условие Липшица, условие Гельдера, Banach space, local convergence, nonlinear equation, Lipschitz condition, HГ¶lder condition
Abstract
The aim of this article is to investigate the local convergence analysis of the multi-step Homeier-like approach in order to approximate the solution of nonlinear equations in Banach spaces, which fulfilled the Lipschitz as well as Hölder continuity condition. The Hölder condition is more relaxer than Lipschitz condition. Also, the existence and uniqueness theorem has been derived and found their error bounds. Numerical examples are available to appear the importance of theoretical discussions.
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