Literature Cited
M. M. Lavrent'ev, On Some Noncorrect Problems of Mathematical Physics [in Russian], Izd. SO AN SSSR, Novosibirsk (1962).
A. N. Tikhonov, “On the regularization of noncorrectly posed problems,” Dokl. Akad. Nauk SSSR,153, 49–52 (1963).
V. K. Ivanov, “On first-order Fredholm integral equations,” Diff. Urav.,3, No. 3, 410–421 (1967).
A. B. Bakushinskii, “A regularization algorithm for linear equations with noncorrect operators,” Dokl. Akad. Nauk SSSR,193, No. 1, 12–14 (1968).
S. Mazur, “Uber schwache Konvergenz in den Raumen,” Studia Math.,4, 128–133 (1933).
V. K. Ivanov, “On the regularization of first-order linear operator equations,” Izv. VUZ, Matematika, No. 10, 50–55 (1967).
O. A. Liskovets, “On the regularization of linear equations in Banach spaces,” Diff. Urav.,4, No. 6, 1136–1139 (1968).
F. E. Browder and B. Anton, “Nonlinear functional equations in Banach spaces and elliptic superegularization,” Math. Z.,105, No. 3, 177–195 (1968).
J. L. Lions, Some Methods of solution of Nonlinear Boundary Value Problems [Russian translation], Mir, Moscow (1972).
S. Cruceanu, “Regularisation pour les problems a operateurs monotones et la methode de Gaberkine,” Comment. Math. Univ. Carol.,12, No. 1, 1–13 (1971).
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).
L. F. Korkina, “On the regularization of first-order operator equations,” Izv. VUZ, Matematika, No. 8, 26–29 (1969).
M. M. Vainberg, Variational Methods and Methods of Monotonic Operators [in Russian], Nauka, Moscow (1972).
G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities [Russian translation], IL, Moscow (1948).
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).
N. Dunford and I. Schwartz, Linear Operators (General Theory) [Russian translation], Mir, Moscow (1968).
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).
Yu. I. Khudak, “On the convergence of regularizing algorithms,” Zh. Vych. Matem. i Matem. Fiz.,11, No. 1, 29–35 (1971).
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).
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).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 16, No. 1, pp. 3–11, January–February, 1975.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00967456