On the monotone convergence of an Euler-Chebysheff-type method in partially ordered topological spaces

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  • Ioannis K. Argyros Cameron University, Lawton, USA
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References

I.K.Argyos, and F. Szidarovszky, On the monotone convergence of general Newton-like metohods,Bull. Austral. Math. Soc., 45, (1992), pp. 489-502, https://doi.org/10.1017/s0004972700030392

I. K. Argyros, and F. Szidarovszky,The Theory and Applications of lteration Methods, C.R.C. Press, Inc. Boca Raton, Florida, U.S.A, (1993).

I. K. Argyros, On the convergence of Chebysheff-Halley-type method under Newton-Kantorovich hypotheses, Appl. Math. Letter, 6, 5, (1993), pp. 71-74, https://doi.org/10.1016/0893-9659(93)90104-u

L .V. Kantorovich, The method of successive approximation for functional equotions, Acta Math., 71 (1939), pp. 63-97, https://doi.org/10.1007/bf02547750

M. A. Mertecova, An analog of the process of tangent hyperbolas for general functional equations (in Russian), Dokl. Akad. Nauk SSSR, 88 (1953), pp. 611-614.

M. T. Necepurenko, On Chebysheff's method for functional equations (in Russian), Usephi Mat. Nauk., 9 (1954). pp.163-170.

F. A. Potra, on an iterative algorithm of order 1.839 .., for solving nonlinear operator equations, Numer. Funct. Anal. Optimiz.,7 (/), (1934-1985), pp.75-106, https://doi.org/10.1080/01630568508816182

S. Ul'm, Iteration methods with divided diferences of the second order (in Russian), Dokl. Akad. Nauk SSSR, 158 (1964), pp. 55-58, Soviet Math. Dokl. 5, pp.1187-1190.

J.A. Vandergraft, Newton's method for convex operators in partially ordered spaces, SIAM J. Numer. Anal. 4 (1967), pp. 406 – 432, https://doi.org/10.1137/0704037

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Published

1998-02-01

How to Cite

Argyros, I. K. (1998). On the monotone convergence of an Euler-Chebysheff-type method in partially ordered topological spaces. Rev. Anal. Numér. Théor. Approx., 27(1), 23–31. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1998-vol27-no1-art4

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