A NEW EXTENSION OF PARAMETER CONTINUATION METHOD FOR SOLVING OPERATOR EQUATIONS OF THE SECOND KIND

Authors

  • Ngo Thanh Binh Nam Dinh University of Technology Education, Vietnam

DOI:

https://doi.org/10.51453/2354-1431/2021/521

Keywords:

Parameter continuation method, Monotone operator, Contractive operator, Operator equations of the second kind, Approximate solution.

Abstract

In this paper, we propose an extension of the parameter continuation method for solving operator equations of the second kind. By splitting of the operator into a sum of two operators: one monotone, Lipschitz-continuous and one contractive, the applicability of the method is broader. The suitability of the proposed approach is presented through an example.

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References

[1] Bernstein, S. N. (1906). Sur la généralisation du problème de Dirichlet, Math. Ann. 62:253–271.

[2] Gaponenko, Y. L. (1986). The parameter – extension method for an equation of the second kind with a Lipschitz – continuous and monotonic operator. Comput. Maths. Math. Phys, 26:1123–1131.

[3] Leray, J., Schauder, J. (1934). Topologi et équations fonctionnelles. Ann. Sci. Éc. Norm. Supér. 51:45–78.

[4] Phat, V.N. (2001). Introduction to mathematical control theory. Vietnam National University Press, Hanoi, Vietnam.

[5] Trenogin, V. A. (1990). Functional Analysis. Nauka, Moscow.

[6] Trenogin, V. A. (1996). Global invertibility of nonlinear operator and the method of continuation with respect to a parameter, Dokl. Akad. Nauk, 350:1–3.

[7] Trenogin, V. A. (1996). Locally invertible operator and parameter continuation method, Funktsional. Anal. i Prilozhen, 30:93–95.

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Published

2021-08-17

How to Cite

Ngô Thanh, B. (2021). A NEW EXTENSION OF PARAMETER CONTINUATION METHOD FOR SOLVING OPERATOR EQUATIONS OF THE SECOND KIND. SCIENTIFIC JOURNAL OF TAN TRAO UNIVERSITY, 7(21). https://doi.org/10.51453/2354-1431/2021/521

Issue

Vol. 7 No. 21 (2021)

Section

Natural Science and Technology

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