The approximation of the solutions of equations using approximant sequences

Adrian Diaconu

doi:10.33993/jnaat321-731

Authors

Adrian Diaconu “Babes-Bolyai” University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat321-731

Keywords:

convergence of the approximant sequences for operatorial equations in Banach spaces

Abstract views: 201

Abstract

We intend to characterize the convergence of a certain sequence that belongs to a subset of a Banach space towards the solution of an equation obtained by the annulment of a nonlinear mapping that is defined on this subset and that takes values in another linear normed space. This mapping has a Fréchet derivative of a certain order which verifies the Lipschitz condition. We can establish some conditions that are enough both for the existence of the equation's solution and for a speed of convergence of a certain order for the approximant sequence.

Downloads

Download data is not yet available.

References

Diaconu, A., Sur quelques méthodes itératives combinées, Mathematica, 22(45), no. 2, pp. 247-261, 1980.

Diaconu, A., Sur la manière d'obtenir et sur la convergence de certaines méthodes itératives, "Babeş-Bolyai" University, Faculty of Mathematics and Phisics, Research Seminars, Seminar on Functional Analysis and Numerical Methods, Preprint Nr. 1, pp. 27-74, 1987.

Diaconu, A., On the approximation of the solution of equations in Banach spaces using approximant sequences, Proceeding of the Conference on Analysis, Functional Equations, Approximation and Convexity in Honor of Professor Elena Popoviciu, Cluj-Napoca, October 15-16, pp. 62-72, 1999.

Diaconu, A., Remarks on the convergence of some iterative methods of the Traub type, Studia Univ. "Babeş--Bolyai", Mathematica, XLII, no. 2, pp. 47-60, 1997.

Kantorovich, L. V., Functionalnîi analiz i pridcladnaia mathematica, U. M. N. III, 6, (28), pp. 89-185, 1948 (in Russian).

Kantorovich, L. V., and Akilov, G. P., Functional Analysis, Editura Ştiinţifică şi Enciclopedică, Bucureşti, 1986 (in Romanian).

Mysovski, I. P., Na shodimosti metoda Newtona, Trudî mat. inst. V., A., Steklova, 28, pp. 145-149, 1949 (in Russian).

Păvăloiu, I., Sur les procédés à un ordre élevé de convergence, Mathematica, Cluj, 12(35), no. 2, pp. 309-324, 1970.

Păvăloiu, I., Introduction to Approximating the Solutions of Equations, Editura Dacia, Cluj-Napoca, 1976 (in Romanian).