×

A family of Chebyshev-Halley type methods in Banach spaces. (English) Zbl 0893.47043

Summary: A family of third-order iterative processes (that includes Chebyshev and Halley’s methods) is studied in Banach spaces. Results on convergence and uniqueness of solutions are given, as well as error estimates. This study allows us to compare the most famous third-order iterative processes.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
65J15 Numerical solutions to equations with nonlinear operators
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1016/0377-0427(88)90389-5 · Zbl 0632.65070
[2] DOI: 10.2307/2322644 · Zbl 0574.65041
[3] DOI: 10.1016/0893-9659(94)90071-X · Zbl 0811.65043
[4] DOI: 10.1016/0096-3003(93)90137-4 · Zbl 0787.65034
[5] Chen, Comment. Math. Univ. Carolin. 34 pp 153– (1993)
[6] DOI: 10.1007/BF02238803 · Zbl 0714.65061
[7] DOI: 10.1007/BF02241866 · Zbl 0701.65043
[8] Argyros, Proyecciones 12 pp 119– (1993)
[9] Altman, Bull. Acad. Pol. Sci., Ser. Sci. Math., Ast. et Phys. 9 pp 633– (1961)
[10] DOI: 10.2307/2321760 · Zbl 0486.65035
[11] DOI: 10.1137/0705003 · Zbl 0155.46701
[12] Rall, Computational solution of nonlinear operator equations (1979)
[13] Ostrowski, Solution of equations in Euclidean and Banach spaces (1943)
[14] Kantorovich, Functional analysis (1982)
[15] DOI: 10.1080/00207169308804162 · Zbl 0812.65038
[16] Hernández, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 22 pp 159– (1993)
[17] DOI: 10.1007/BF01385780 · Zbl 0712.65035
[18] DOI: 10.1080/00207169508804427 · Zbl 0844.47035
[19] Döring, Aplikace Mat. 15 pp 418– (1970)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.