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On the solution of nonlinear equations with monotone opera tors in a Banach space

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Literature Cited

  1. M. M. Lavrent'ev, On Some Noncorrect Problems of Mathematical Physics [in Russian], Izd. SO AN SSSR, Novosibirsk (1962).

    Google Scholar 

  2. A. N. Tikhonov, “On the regularization of noncorrectly posed problems,” Dokl. Akad. Nauk SSSR,153, 49–52 (1963).

    Google Scholar 

  3. V. K. Ivanov, “On first-order Fredholm integral equations,” Diff. Urav.,3, No. 3, 410–421 (1967).

    Google Scholar 

  4. A. B. Bakushinskii, “A regularization algorithm for linear equations with noncorrect operators,” Dokl. Akad. Nauk SSSR,193, No. 1, 12–14 (1968).

    Google Scholar 

  5. S. Mazur, “Uber schwache Konvergenz in den Raumen,” Studia Math.,4, 128–133 (1933).

    Google Scholar 

  6. V. K. Ivanov, “On the regularization of first-order linear operator equations,” Izv. VUZ, Matematika, No. 10, 50–55 (1967).

    Google Scholar 

  7. O. A. Liskovets, “On the regularization of linear equations in Banach spaces,” Diff. Urav.,4, No. 6, 1136–1139 (1968).

    Google Scholar 

  8. F. E. Browder and B. Anton, “Nonlinear functional equations in Banach spaces and elliptic superegularization,” Math. Z.,105, No. 3, 177–195 (1968).

    Google Scholar 

  9. J. L. Lions, Some Methods of solution of Nonlinear Boundary Value Problems [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  10. S. Cruceanu, “Regularisation pour les problems a operateurs monotones et la methode de Gaberkine,” Comment. Math. Univ. Carol.,12, No. 1, 1–13 (1971).

    Google Scholar 

  11. A. B. Bakushinskii, “On the problem of the construction of linear regularizing algorithms in Banach spaces,” Zh. Vych. Matem. i Matem. Fiz.,13, No. 1, 204–209 (1973).

    Google Scholar 

  12. L. F. Korkina, “On the regularization of first-order operator equations,” Izv. VUZ, Matematika, No. 8, 26–29 (1969).

    Google Scholar 

  13. M. M. Vainberg, Variational Methods and Methods of Monotonic Operators [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  14. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities [Russian translation], IL, Moscow (1948).

    Google Scholar 

  15. G. I. Minty, “On a monotonicity method for the solution of nonlinear equations in Banach spaces,” Proc. Nat. Acad. Sci. USA,53, 1038–1041 (1963).

    Google Scholar 

  16. N. Dunford and I. Schwartz, Linear Operators (General Theory) [Russian translation], Mir, Moscow (1968).

    Google Scholar 

  17. V. P. Maslov, “The existence of a solution of a noncorrect problem is equivalent to the convergence of a regularized proces,” Usp. Matem. Nauk,23, No. 3, 183–184 (1968).

    Google Scholar 

  18. Yu. I. Khudak, “On the convergence of regularizing algorithms,” Zh. Vych. Matem. i Matem. Fiz.,11, No. 1, 29–35 (1971).

    Google Scholar 

  19. V. A. Morozov, “On a residual principle for the solution of operator equations by a regularization method,” Zh. Vych. Matem. i Matem. Fiz.,8, No. 2, 295–309 (1968).

    Google Scholar 

  20. L. A. Kalyakin, “On the approximate solution of noncorrect problems in normed spaces,” Zh. Vych. Matem. i Matem. Fiz.,12, No. 5, 1168–1181 (1972).

    Google Scholar 

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 16, No. 1, pp. 3–11, January–February, 1975.

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Al'ber, Y.I. On the solution of nonlinear equations with monotone opera tors in a Banach space. Sib Math J 16, 1–8 (1975). https://doi.org/10.1007/BF00967456

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