ON THE MONOTONE CONVERGENCE OF SOME ITERATIVE PROCEDURES IN PARTIALLY ORDERED BANACH SPACES

Authors

  • IOANNIS K. ARGYROS Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003.

DOI:

https://doi.org/10.5556/j.tkjm.21.1990.4673

Keywords:

Monotone convergence, Banach space

Abstract

We provide some enclosure methods for the solution of a nonlinear equation in a partially ordered Banach space. By using a certain projection operator we show that the solution can be obtained from the solution of a system of linear algebraic equations.

References

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Kantorovich, L. V. The method of successive approximation for functional equations. Acta Math. 71, (1939), 63-97.

Ortega, J.M. and Rheinholdt, W.C. Iterative solution of nonlinear equations in several variables. Academic Press, New York, (1970).

Potra, F.A. Newton-like methods with monotone convergence for solving nonlinear operator equations. Nonlinear analysis theory methods and application. Vol. 11, 6, (1987), 697-717.

Schmidt, J.W . and Leonhardt, H. Eingrenzung von Losungen mit Hilfe der Regula falsi. Computing, 6 (1970), 318-329.

Vanderfraft, J.S. Newton's method for convex operators in partially ordered spaces. SIAM J. Numer. Anal. 4, (1967), 402-432.

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Published

1990-09-01

How to Cite

ARGYROS, I. K. (1990). ON THE MONOTONE CONVERGENCE OF SOME ITERATIVE PROCEDURES IN PARTIALLY ORDERED BANACH SPACES. Tamkang Journal of Mathematics, 21(3), 269–277. https://doi.org/10.5556/j.tkjm.21.1990.4673

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