Ball Convergence of Modified Homeier-Like's Method in Banach Spaces under Weak Continuity Condition

Authors

  • Neha Gupta
  • J. P. Jaiswal

DOI:

https://doi.org/10.18311/jims/2022/26313

Keywords:

Banach Space, Lcal Cconvergence, Recurrence Relation, β-Continuity condition.

Abstract

The aim of this study is to analyze the local convergence of the multi-step Homeier's-like method for solving nonlinear equations in Banach space. Furthermore, we avoid hypotheses on high order derivatives which limit the applicability of the method. Instead, we only use hypotheses on the first derivative. Thus the applicability of the method has been extended by preserving the order of convergence. The convergence of the solution is proved under the weak hypotheses i.e. $\omega$-continuity condition. Some numerical instances where earlier results cannot be applied to solve equations but our results can be applied are provided to validate the theoretical contribution.

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Published

2022-08-23

How to Cite

Gupta, N., & Jaiswal, J. P. (2022). Ball Convergence of Modified Homeier-Like’s Method in Banach Spaces under Weak Continuity Condition. The Journal of the Indian Mathematical Society, 89(3-4), 305–316. https://doi.org/10.18311/jims/2022/26313