ON SOME PROJECTION METHODS FOR APPROXIMATING FIXED POINTS OF NONLINEAR EQUATIONS IN BANACH SPACE

Authors

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

DOI:

https://doi.org/10.5556/j.tkjm.21.1990.4682

Keywords:

Fixed point, Banach space, Neton-like method

Abstract

We use a Newton-like method to approximate a fixed point of a non- linear operator equation in a Banach space. Our iterates are computed at each step by solving a linear algebraic system of finite order.

References

Argyros, I. K. "Newton-like methods under mild differentiablity conditions with error analysis," Bull. Austral, Math. Soc., Vol. 37, 2, (1987), 131-147.

----, "Concerning the approximate solutions of operator equations in Hilbert space under mild differentiability conditions", Tamkang J. Math. Vol. 19, 4, (1985), 7-19.

Dennis, J.E., "Toward a unified convergence theory of Newton-like methods", In Nonlinear Functional Analysis and Applications (edited by L.B. Rall), Academic Press, New York, 1971.

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

Kurnel, N. S. and Migovich, F. M., "Some Generalizations of the Newton-Kantorovich method", Ukrainskii Mathematicheskii Zhurnal, Vol. 21, No. 5 (1969), 948-960.

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

Zabreiko, P. P. and Nguen, D. F., "The majorant method in the theory of Newton-Kantorovich approximations and the Ptak error esimates", Numer. Funct. Anal. and Optimiz. 9 (5 and 6), (1987), 671-684.

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Published

1990-12-01

How to Cite

ARGYROS, I. K. (1990). ON SOME PROJECTION METHODS FOR APPROXIMATING FIXED POINTS OF NONLINEAR EQUATIONS IN BANACH SPACE. Tamkang Journal of Mathematics, 21(4), 351–357. https://doi.org/10.5556/j.tkjm.21.1990.4682

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