Geodesic
Convexity properties of images under nonlinear integral operators
Sbornik. Mathematics, Tome 205 (2014) no. 12, pp. 1775-1786 Cet article a éte moissonné depuis la source Math-Net.Ru

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Conditions are obtained for the image of a given set under a general completely continuous nonlinear integral operator to have convex closure. These results are used to establish the uniqueness of quasi-solutions of nonlinear integral equations of the first kind and to prove the solvability of equations of the first kind on a dense subset of the right-hand sides. Bibliography: 11 titles.
Keywords: nonlinear integral operator, image of a set, closure, convexity, equation of the first kind. 
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M. Yu. Kokurin. Convexity properties of images under nonlinear integral operators. Sbornik. Mathematics, Tome 205 (2014) no. 12, pp. 1775-1786. http://geodesic.mathdoc.fr/item/SM_2014_205_12_a5/

[1] R. T. Rockafellar, “Convexity properties of nonlinear maximal monotone operators”, Bull. Amer. Math. Soc., 75:1 (1969), 74–77 | DOI | MR | Zbl

[2] F. E. Browder, “Normal solvability and $\phi$-accretive mappings of Banach spaces”, Bull. Amer. Math. Soc., 78:2 (1972), 186–192 | DOI | MR | Zbl

[3] A. S. Matveev, “On the convexity of the images of quadratic mappings”, St. Petersburg Math. J., 10:2 (1999), 343–372 | MR | Zbl

[4] V. L. Levin, Vypuklyi analiz v prostranstvakh izmerimykh funktsii i ego primenenie v matematike i ekonomike, Nauka, M., 1985, 352 pp. | MR | Zbl

[5] Yu. G. Borisovich, B. D. Gelman, A. D. Myshkis, V. V. Obukhovskii, Vvedenie v teoriyu mnogoznachnykh otobrazhenii i differentsialnykh vklyuchenii, KomKniga, M., 2005, 215 pp. | MR | Zbl

[6] A. A. Lyapunov, “O vpolne additivnykh vektor-funktsiyakh”, Izv. AN SSSR. Ser. matem., 4:6 (1940), 465–478 | MR | Zbl

[7] V. M. Alekseev, V. M. Tikhomirov, S. V. Fomin, Optimal control, Contemp. Soviet Math., Consultants Bureau, New York, 1987, xiv+309 pp. | DOI | MR | Zbl

[8] P. P. Zabrejko, A. I. Koshelev, M. A. Krasnosel'skij, S. G. Mikhlin, L. S. Rakovshchik, V. Ya. Stet'senko, Integral equations, Noordhoff International Publishing, Leyden, 1975, xix+443 pp. | Zbl | Zbl

[9] S. I. Kabanikhin, Obratnye i nekorrektnye zadachi, Sib. nauch. izd-vo, Novosibirsk, 2008, 460 pp.

[10] A. B. Bakushinskii, M. Yu. Kokurin, Iteratsionnye metody resheniya nekorrektnykh operatornykh uravnenii s gladkimi operatorami, Editorial URSS, M., 2002, 192 pp.

[11] V. K. Ivanov, V. V. Vasin, V. P. Tanana, Theory of linear ill-posed problems and its applications, Inverse Ill-posed Probl. Ser., VSP, Utrecht, 2002, xiii+281 pp. | MR | MR | Zbl | Zbl