Skip to main content
Log in

Sufficient conditions for convergence of modified projection-iterative method for equations with weak nonlinearity

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

New sufficient conditions are established for the convergence of the modified projection-iterative method for operator equations in a Banach space with weak nonlinearity, less restrictive than those known in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. A. Yu. Luchka, Theory and Application of the Method of Averaging Functional Corrections [in Russian], Izdat. Akad. Nauk UkrSSR, Kiev (1963).

    Google Scholar 

  2. A. Yu. Luchka, Projection-Iterative Methods of Solution of Differential and Integral Equations [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  3. Yu. D. Sokolov, Method of Averaging Functional Corrections [in Russian], Naukova Dumka, Kiev (1967).

    Google Scholar 

  4. N. S. Kurpel', Projection-Iterative Methods of Solution of Operator Equations [in Russian], Naukova Dumka, Kiev (1968).

    Google Scholar 

  5. A. Yu. Luchka, “Tests for convergence of the projection-iterative method for nonlinear equations,” Preprint Inst. Mat., Akad. Nauk UkrSSR, Kiev (1982).

    Google Scholar 

  6. A. Yu. Luchka and Ya. I. Yarmush, “Solution of a system of finite-difference equations with small nonlinearity by the projection-iterative method,” Preprint, Inst. Mat., Akad. Nauk UkrSSR, Kiev (1979), pp. 20–30.

    Google Scholar 

  7. A. Yu. Luchka and L. S. Voznyak, “Application of a modification of the projection-iterative method to a singular integral equatin with small nonlinearity,” in: Differential-Difference Equations and Problems of Mathematical Physics [in Russian], Inst. Mat., Akad. Nauk UkrSSR, Kiev (1984), pp. 43–49.

    Google Scholar 

  8. S. A. Kril', “Soluton of integro-difference equations with small nonlinearity by the projection-iterative method,” Preprint, Inst. Mat., Akad. Nauk UkrSSR, Kiev (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1486–1492, November, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Luchka, A.Y. Sufficient conditions for convergence of modified projection-iterative method for equations with weak nonlinearity. Ukr Math J 42, 1328–1335 (1990). https://doi.org/10.1007/BF01066188

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01066188

Keywords

Navigation