Geodesic
Semilocal convergence analysis for a three-step scheme in Banach spaces with a new type majorant: using average Lipschitz conditions
J. P. Jaiswal1 ; Akanksha Saxena2 ; K. R. Pardasani2 ; I. K. Argyros3
1 Department of Mathematics Guru Ghasidas Vishwavidyalaya (A Central University) Bilaspur, C.G., India 495009
2 Department of Mathematics Maulana Azad National Institute of Technology Bhopal, M.P., India 462003
3 Department of Mathematical Sciences Cameron University Lawton, OK 73505, USA
Applicationes Mathematicae, Tome 51 (2024) no. 2, pp. 179-203.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We analyze the semilocal convergence (S.C.) of the Newton-Traub scheme (NTS) used for finding solutions of nonlinear problems in Banach spaces. The analysis is based on the assumption that a generalized Lipschitz condition is satisfied by the first derivative of the relevant operator. The analysis establishes the fifth-order convergence of the NTS under an additional condition. Furthermore, we consider two special cases. The findings contribute to the theoretical understanding of NTS in Banach spaces and have practical applications, for example to integral equations.
DOI : 10.4064/am2477-5-2024
Keywords: analyze semilocal convergence newton traub scheme nts finding solutions nonlinear problems banach spaces analysis based assumption generalized lipschitz condition satisfied first derivative relevant operator analysis establishes fifth order convergence nts under additional condition furthermore consider special cases findings contribute theoretical understanding nts banach spaces have practical applications example integral equations

J. P. Jaiswal 1 ; Akanksha Saxena 2 ; K. R. Pardasani 2 ; I. K. Argyros 3

1 Department of Mathematics Guru Ghasidas Vishwavidyalaya (A Central University) Bilaspur, C.G., India 495009
2 Department of Mathematics Maulana Azad National Institute of Technology Bhopal, M.P., India 462003
3 Department of Mathematical Sciences Cameron University Lawton, OK 73505, USA 
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J. P. Jaiswal; Akanksha Saxena; K. R. Pardasani; I. K. Argyros. Semilocal convergence analysis for a three-step scheme in Banach spaces with a new type majorant: using average Lipschitz conditions. Applicationes Mathematicae, Tome 51 (2024) no. 2, pp. 179-203. doi : 10.4064/am2477-5-2024. http://geodesic.mathdoc.fr/articles/10.4064/am2477-5-2024/

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