On an Efficient Iterative Method for Fixed Points

Authors

  • Mukund Mohan Department of Mathematics, Lalit Narayan Mithila University, Darbhanga, Bihar, 846004, India
  • Abhimanyu Kumar Department of Mathematics, Lalit Narayan Mithila University, Darbhanga, Bihar, 846004, India
  • S. N. Roy Department of Mathematics, Lalit Narayan Mithila University, Darbhanga, Bihar, 846004, India
  • P. K. Parida Department of Mathematics, Central University of Jharkhand, Ranchi-835205, India

DOI:

https://doi.org/10.37256/cm.4420232755

Keywords:

midpoint method, Striling method, order of convergence, local convergence, semilocal convergence, Lipschitz and center-Lipschitz condition

Abstract

Real-world applications depend heavily on the fixed-point solution. In this paper, we have suggested an effective iterative method for fixed points. We have first given the approximate order of convergence for this method using Taylor’s series. The radii of convergence balls for this method can then be calculated using a local convergence theorem that we then present. The semilocal convergence theorem, which determines the starting point’s accuracy, is then presented. We have created some technical lemmas and theorems to serve this purpose. In contrast to an earlier study using the same type of method for nonlinear equations, we have not used the convergence conditions on higher-order Frechet derivatives in our study of convergence. Finally, some numerical examples are provided to support the theoretical findings we made. This highlights the uniqueness of this study.

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Published

2023-12-19

How to Cite

1.
Mohan M, Kumar A, Roy SN, Parida PK. On an Efficient Iterative Method for Fixed Points. Contemp. Math. [Internet]. 2023 Dec. 19 [cited 2024 Dec. 10];4(4):1260-78. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2755