×

zbMATH — the first resource for mathematics

A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact mappings. (English) Zbl 0297.47049

MSC:
47H10 Fixed-point theorems
55M25 Degree, winding number
47J05 Equations involving nonlinear operators (general)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] H. F. Bohnenblust and S. Karlin, On a theorem of Ville, Contributions to the Theory of Games, Annals of Mathematics Studies, no. 24, Princeton University Press, Princeton, N. J., 1950, pp. 155 – 160. · Zbl 0041.25701
[2] Felix E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041 – 1044. · Zbl 0128.35801
[3] Felix E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R. I., 1976, pp. 1 – 308.
[4] Arrigo Cellina and Andrzej Lasota, A new approach to the definition of topological degree for multi-valued mappings, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 47 (1969), 434 – 440 (1970) (English, with Italian summary). · Zbl 0194.44801
[5] Josef Daneš, Some fixed point theorems, Comment. Math. Univ. Carolinae 9 (1968), 223 – 235. · Zbl 0165.49201
[6] Gabriele Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova 24 (1955), 84 – 92 (Italian). · Zbl 0064.35704
[7] D. G. de Figueiredo and L. A. Karlovitz, On the radial projection in normed spaces, Bull. Amer. Math. Soc. 73 (1967), 364 – 368. · Zbl 0172.16102
[8] J. Dugundji, An extension of Tietze’s theorem, Pacific J. Math. 1 (1951), 353 – 367. · Zbl 0043.38105
[9] Massimo Furi and Alfonso Vignoli, On \?-nonexpansive mappings and fixed points, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 48 (1970), 195 – 198 (English, with Italian summary). · Zbl 0197.11806
[10] I. L. Glicksberg, A further generalization of the Kakutani fixed theorem, with application to Nash equilibrium points, Proc. Amer. Math. Soc. 3 (1952), 170 – 174. · Zbl 0046.12103
[11] Dietrich Göhde, Zum Prinzip der kontraktiven Abbildung, Math. Nachr. 30 (1965), 251 – 258 (German). · Zbl 0127.08005
[12] I. C. Gohberg, L. S. Gol’denšteĭn, and A. S. Markus, Investigations of some properties of bounded linear operators with their q-norms, Kišinev, Gos. Univ. Učen. Zap. 29 (1957), 29-36.
[13] A. Granas, Sur la notion du degré topologique pour une certaine classe de transformations multivalentes dans les espaces de Banach, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 7 (1959), 191 – 194 (unbound insert) (French, with Russian summary). · Zbl 0087.32303
[14] A. Granas, Theorem on antipodes and theorems on fixed points for a certain class of multi-valued mappings in Banach spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 7 (1959), 271 – 275 (unbound insert) (English, with Russian summary). · Zbl 0089.11202
[15] C. J. Himmelberg, J. R. Porter, and F. S. Van Vleck, Fixed point theorems for condensing multifunctions, Proc. Amer. Math. Soc. 23 (1969), 635 – 641. · Zbl 0195.14902
[16] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004 – 1006. · Zbl 0141.32402
[17] C. Kuratowski, Sur les espaces complets, Fund. Math. 15 (1930), 301-309. · JFM 56.1124.04
[18] Ky. Fan, Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 121 – 126. · Zbl 0047.35103
[19] E. Lami Dozo, Opérateurs nonexpansifs, P-compact, et propriétés géométriques de la norme, Doctoral Dissertation, Univ. Libre de Bruxelles, 1970.
[20] A. Lasota and Z. Opial, Fixed-point theorems for multi-valued mappings and optimal control problems, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 645 – 649 (English, with Loose Russian summary). · Zbl 0165.43304
[21] E. A. Lifšic and B. N. Sadovskiĭ, A fixed point theorem for generalized condensing operators, Dokl. Akad. Nauk SSSR 183 (1968), 278 – 279 (Russian).
[22] Tsoy-wo Ma, Topological degrees of set-valued compact fields in locally convex spaces, Dissertationes Math. Rozprawy Mat. 92 (1972), 43. · Zbl 0211.25903
[23] Jack T. Markin, A fixed point theorem for set valued mappings, Bull. Amer. Math. Soc. 74 (1968), 639 – 640. · Zbl 0159.19903
[24] Sam B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475 – 488. · Zbl 0187.45002
[25] R. D. Nussbaum, The fixed point index and fixed point theorems for k-set-contractions, Doctoral Dissertation, University of Chicago, Chicago, Ill., 1969. · Zbl 0174.45402
[26] Roger D. Nussbaum, The fixed point index for local condensing maps, Ann. Mat. Pura Appl. (4) 89 (1971), 217 – 258. · Zbl 0226.47031
[27] Zdzisław Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591 – 597. · Zbl 0179.19902
[28] W. V. Petryshyn, Structure of the fixed points sets of \?-set-contractions, Arch. Rational Mech. Anal. 40 (1970/1971), 312 – 328. · Zbl 0218.47028
[29] W. V. Petryshyn, A new fixed point theorem and its application, Bull. Amer. Math. Soc. 78 (1972), 225 – 229. · Zbl 0231.47030
[30] W. V. Petryshyn, Fixed point theorems for various classes of 1-set-contractive and 1-ball-contractive mappings in Banach spaces, Trans. Amer. Math. Soc. 182 (1973), 323 – 352. · Zbl 0277.47033
[31] Simeon Reich, Fixed points in locally convex spaces, Math. Z. 125 (1972), 17 – 31. · Zbl 0216.17302
[32] B. N. Sadovskiĭ, Measures of noncompactness and condensing operators, Problemy Mat. Anal. Slož. Sistem 2 (1968), 89 – 119 (Russian).
[33] -, Ultimately compact and condensing mappings, Uspehi Mat. Nauk 27 (1972), 81-146. (Russian)
[34] Helmut H. Schaefer, Topological vector spaces, Springer-Verlag, New York-Berlin, 1971. Third printing corrected; Graduate Texts in Mathematics, Vol. 3. · Zbl 0212.14001
[35] G. M. Vaĭnikko and B. N. Sadovskiĭ, On the degree of (ball) condensing vector fields, Problemy Mat. Anal. Slož. Sistem 2 (1968), 84-88. (Russian)
[36] P. P. Zabreĭko and M. A. Krasnosel’skiĭ, A method for producing new fixed point theorems, Dokl. Akad. Nauk SSSR 176 (1967), 1233-1235 = Soviet Math. Dokl. 8 (1967), 1297-1299. MR 36 #3183.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.