Open AccessExtending the Applicability and Convergence Domain of a Fifth-Order Iterative Scheme under Hölder Continuous Derivative in Banach Spaces
Author(s) -
Debasis Sharma,
Sanjaya Kumar Parhi,
Shanta Kumari Sunanda
Publication year - 2021
Publication title -
contemporary mathematics
Language(s) - English
Resource type - Journals
eISSN - 2705-1064
pISSN - 2705-1056
DOI - 10.37256/cm.242021962
Subject(s) - lipschitz continuity , mathematics , convergence (economics) , domain (mathematical analysis) , fréchet derivative , derivative (finance) , banach space , solver , operator (biology) , hölder condition , mathematical analysis , lipschitz domain , nonlinear system , order (exchange) , constant (computer programming) , mathematical optimization , computer science , programming language , biochemistry , chemistry , physics , finance , repressor , quantum mechanics , transcription factor , financial economics , economics , gene , economic growth
The most significant contribution made by this study is that the applicability and convergence domain of a fifth-order convergent nonlinear equation solver is extended. We use Hölder condition on the first Fréchet derivative to study the local analysis, and this expands the applicability of the formula for such problems where the earlier study based on Lipschitz constants cannot be used. This study generalizes the local analysis based on Lipschitz constants. Also, we avoid the use of the extra assumption on boundedness of the first derivative of the involved operator. Finally, numerical experiments ensure that our analysis expands the utility of the considered scheme. In addition, the proposed technique produces a larger convergence domain, in comparison to the earlier study, without using any extra conditions.