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The method of successive approximations for functional equations. (English) Zbl 0021.13604

[1]Akbergenoff, I. A. On the Approximate Solution of Integral Equations of Fredholm and on the Determination of their Proper Values (in Russian). Recueil Mathém. 42 (1933), pp. 679–698.
[2]Banach, S. I. Théorie des opérations linéaires. Warszawa 1932.–II. Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales. Fund. Math. III, 1922.
[3]Cacciopoli, I. Un theorema generale sull’esistenza di elementi uniti in una transformazione funzionale. Rend. Lincei t. XI, 1930.
[4]Dixon, Cambr. Trans. 19 (1902), pp. 190–233.
[5]Kantorovitch, L. I. On a Class of Functional Equations. C.R. de l’Ac. des Sc. USSR IV (XIII) 1936, pp. 219–224.–Kantorovitch, L. II. Lineare halbgeordnete Räume. Recueil Mathém. t. 2 (44), pp. 121–168.–Kantorovitch, L. III. Sur la théorie générale des opérations dans les espaces semi-ordonnés. C. R. Ac. USSR I (X) (1936), pp. 213–286.–Kantorovitch, L. IV. Allgemeine Formen gewisser Klassen von linearen Operationen. Ibid. C. R. Ac. USSR III (XII) (1936), pp. 101–106.
[6]Kantorovitch, L. & Kryloff, V. Methods of an Approximate Solution of Partial Differential equations (in Russian). Leningrad 1936.
[7]von Koch, Helge. I. Jahresb. d. Deutsch. Math. Ver. 22 (1913), pp. 285–291. –von Koch, Helge. II. Acta Math., 16 (1892), pp. 217–295.–von Koch, Helge. III. Ibid. Acta Math., 24 (1900), pp. 89–122. –von Koch, Helge. IV. Palermo Rend., 28 (1909), pp. 255–266.
[8]Koyalovitch, B. Researches on the Infinite Systems of Linear Equations. Travaux de l’Inst. Mathém. de Stekloff (in Russian). III. (1930), pp. 41–167.
[9]Kuzmin, Researches on a Class of Infinite Systems of Linear Equations. Bull. de l’Ac. des Sciences de l’URSS; 1934, No 4, pp. 515–546.
[10]Niemytzkie, I. On a Class of Non-linear Integral Equations. Rev. Math. 41 (1934), pp. 655–658.
[11]Ostrowski, A. Konvergenz-Diskussion und Fehlerabschätzung für die Newton’sche Methode bei Gleichungssysteme. Comment. Math. helv. 9 (1937), pp. 79–103. · doi:10.1007/BF01258177
[12]Pellet, A. I. Des équations majorantes. Bull. Soc. Math. de France (1909), pp. 93–101.–Pellet, A. II. Des systèmes infinies d’équations Ibid. Bull. Soc. Math. de France (1913), pp. 119–126. –Pellet, A. III. Sur la méthode des réduites. Ibid. Bull. Soc. Math. de France (1914), pp. 48–53.
[13]v. Scarborough. Numerical methods of Mathematical Analysis.
[14]Stenin, N. Evaluation of Parameters in the Integral of Christoffel-Schwarz. (In the book “Conform Transformations of Simple Connexes and Multiconnexes Regions” “in Russian”.) Leningrad 1937.
[15]De la Vallé-Poussin, Ch. J. Cours d’Analyse infinitésimale, t. I. Louvain 1913.
[16]Wintner, A. I. Zur Hillschen Theorie der Variation des Mondes. Math. Zeitschr. 24 (1925/26), pp. 259–265.–Wintner, A. II. Ein Satz über unendliche Systeme von linearen Gleichungen. Ibid. Math. Zeitschr., p. 266. · Zbl 02594872 · doi:10.1007/BF01216781