Geodesic
Extending the applicability of a seventh-order method for equations under generalized conditions
Samundra Regmi 1   ; Ioannis K. Argyros 2   ; Santhosh George 3   ; Christopher Argyros 4
1 Department of Mathematics University of Houston Houston, TX 77204, USA <a href="https://orcid.org/0000-0003-0035-1022">ORCID: 0000-0003-0035-1022</a>
2 Department of Computing and Mathematical Sciences Cameron University Lawton, OK 73505, USA <a href="https://orcid.org/0000-0003-1609-3195">ORCID: 0000-0003-1609-3195</a>
3 Department of Mathematical and Computational Sciences National Institute of Technology Karnataka Mangalore, Karnataka, India 575025 <a href="https://orcid.org/0000-0002-3530-5539">ORCID: 0000-0002-3530-5539</a>
4 Department of Computing and Mathematical Sciences Cameron University Lawton, OK 73505, USA <a href="https://orcid.org/0000-0002-7647-3571">ORCID: 0000-0002-7647-3571</a>
Applicationes Mathematicae, Tome 50 (2023) no. 2, pp. 167-175 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We extend the applicability of a seventh-order method for solving Banach space-valued equations. This is achieved by using generalized conditions on the first derivative which only appears in the method. Earlier works use conditions up to the eighth derivative to establish convergence. Our technique is very general and can be used to extend the applicability of other methods along the same lines.
DOI : 10.4064/am2439-2-2023
Keywords: extend applicability seventh order method solving banach space valued equations achieved using generalized conditions first derivative which only appears method earlier works conditions eighth derivative establish convergence technique general extend applicability other methods along lines

Samundra Regmi  1   ; Ioannis K. Argyros  2   ; Santhosh George  3   ; Christopher Argyros  4

1 Department of Mathematics University of Houston Houston, TX 77204, USA <a href="https://orcid.org/0000-0003-0035-1022">ORCID: 0000-0003-0035-1022</a>
2 Department of Computing and Mathematical Sciences Cameron University Lawton, OK 73505, USA <a href="https://orcid.org/0000-0003-1609-3195">ORCID: 0000-0003-1609-3195</a>
3 Department of Mathematical and Computational Sciences National Institute of Technology Karnataka Mangalore, Karnataka, India 575025 <a href="https://orcid.org/0000-0002-3530-5539">ORCID: 0000-0002-3530-5539</a>
4 Department of Computing and Mathematical Sciences Cameron University Lawton, OK 73505, USA <a href="https://orcid.org/0000-0002-7647-3571">ORCID: 0000-0002-7647-3571</a> 
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     title = {Extending the applicability of a seventh-order method for equations under generalized conditions},
     journal = {Applicationes Mathematicae},
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Samundra Regmi; Ioannis K. Argyros; Santhosh George; Christopher Argyros. Extending the applicability of a seventh-order method for equations under generalized conditions. Applicationes Mathematicae, Tome 50 (2023) no. 2, pp. 167-175. doi: 10.4064/am2439-2-2023

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