×
Nussbaum, Roger D.

Degree theory for local condensing maps. (English) Zbl 0232.47062

J. Math. Anal. Appl. 37, 741-766 (1972).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0232.47062

Cited in 1 Review
Cited in 59 Documents

MSC:

47H11 Degree theory for nonlinear operators
47H10 Fixed-point theorems
55M25 Degree, winding number
55M20 Fixed points and coincidences in algebraic topology
PDF BibTeX XML Cite
\textit{R. D. Nussbaum}, J. Math. Anal. Appl. 37, 741--766 (1972; Zbl 0232.47062)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Alexandroff, P; Hopf, H, Topologie, (1935), J. Springer Berlin · JFM 61.0602.07
[2] Belluce, L.P; Kirk, W.A, Nonexpansive mappings and fixed points in Banach spaces, Illinois J. math., 11, 474-479, (1967) · Zbl 0149.10702
[3] Belluce, L.P; Kirk, W.A; Steiner, E.F, Normal structure in Banach spaces, Pacific J. math., 26, 433-440, (1968) · Zbl 0164.15001
[4] Borisovic, Ju.G; Sapronov, Ju.I, A contribution to the topological theory of condensing operators, Soviet math. dokl., 9, 1304-1307, (1968) · Zbl 0176.45402
[5] Brodskii, M.S; Milman, D.P; Brodskii, M.S; Milman, D.P, On the center of a convex set, Dokl. akad. nauk SSSR, Mr, 9, 448-840, (1948)
[6] Browder, F.E, On the fixed point index for continuous mappings of locally connected spaces, Summa brasil. math., 4, 253-293, (1960)
[7] Browder, F.E, Nonexpansive nonlinear operators in a Banach space, (), 1041-1044 · Zbl 0128.35801
[8] Browder, F.E, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. amer. math. soc., 74, 660-665, (1968) · Zbl 0164.44801
[9] Browder, F.E, Nonlinear operators and nonlinear equations of evolution in Banach spaces, (), to appear · Zbl 0176.45301
[10] Browder, F.E; Nussbaum, R.D, The topological degree for noncompact nonlinear mappings in Banach spaces, Bull. amer. math. soc., 74, 671-676, (1968) · Zbl 0164.17002
[11] Browder, F.E; Petryshyn, W.V, Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces, J. functional analysis, 3, 217-245, (1969) · Zbl 0177.42702
[12] Darbo, G, Punti uniti in trasformazioni a condiminio non compatto, (), 84-92 · Zbl 0064.35704
[13] Dold, A, Fixed point index and fixed point theorems for Euclidean neighborhood retracts, Topology, 4, 1-8, (1965) · Zbl 0135.23101
[14] Dugundji, J, An extension of Tietze’s theorem, Pacific J. math., 1, 353-367, (1951) · Zbl 0043.38105
[15] Gohberg, I.T; Goldenstein, L.S; Markus, A.S, Investigation of some properties of bounded linear operators in connection with their q-norms (in Russian), Uch. zap. kishinevsk. un-ta, 29, 29-36, (1957)
[16] Göhde, D, Zum prinzip der kontraktiven abbildung, Math. nachr., 30, 251-258, (1966) · Zbl 0127.08005
[17] Goldenstein, L.S; Markus, A.S; Goldenstein, L.S; Markus, A.S, On a measure of noncompactness of bounded sets and linear operators, (), Mr, 35, 789-54, (1968), (Russian)
[18] Granas, A, Introduction to topology of functional spaces, Univ. Chicago math. lecture notes, (Spring, 1961)
[19] Hu, S.T, Theory of retracts, (1965), Wayne State Univ. Press Detroit · Zbl 0137.01701
[20] Kirk, W.A, A fixed point theorem for mappings which do not increase distance, Amer. math. monthly, 72, 1004-1006, (1965) · Zbl 0141.32402
[21] Kuratowski, C, Sur LES espaces complets, Fund. math., 15, 301-309, (1930) · JFM 56.1124.04
[22] Leray, J, Sur LES équations et LES transformations, J. math. pures appl., 24, 201-248, (1945) · Zbl 0060.40705
[23] Leray, J; Schauder, J, Topologie et équations fonctionelles, Ann. sci. éc. norm. sup., 51, 45-78, (1934) · JFM 60.0322.02
[24] Nagumo, M, A theory of degree of mapping based on infinitesimal analysis, Amer. J. math., 73, 485-496, (1951) · Zbl 0043.17802
[25] Nagumo, M, Degree of mapping in convex linear topological spaces, Amer. J. math., 73, 497-511, (1951) · Zbl 0043.17801
[26] Nussbaum, R.D, The fixed point index and asymptotic fixed point theorems for k-set-contractions, Bull. amer. math. soc., 75, 490-495, (1969) · Zbl 0174.45402
[27] {\scR. D. Nussbaum}, The fixed point index for local condensing maps, Ann. Matematica, to appear. · Zbl 0226.47031
[28] Nussbaum, R.D, Asymptotic fixed point theorems for local condensing maps, Math. ann., 191, 181-195, (1971) · Zbl 0202.54004
[29] Nussbaum, R.D, The fixed point index and fixed point theorems for k-set contractions, (1969), Univ. Chicago, Unpublished Ph.D. dissertation · Zbl 0174.45402
[30] Nussbaum, R.D, The radius of the essential spectrum, Duke math. J., 38, 473-478, (1970) · Zbl 0216.41602
[31] O’Neill, B, Essential sets and fixed points, Amer. J. math., 75, 497-509, (1953) · Zbl 0050.39202
[32] Petryshyn, W.V, On the approximation-solvability of nonlinear equations, Math. ann., 177, 156-164, (1968) · Zbl 0162.20301
[33] Petryshyn, W.V, On the projectional-solvability and the Fredholm alternative for equations involving linear A-proper operators, Arch. rational mech. anal., 30, 270-284, (1968) · Zbl 0176.45902
[34] Petryshyn, W.V, Nonlinear equations involving noncompact operators, (), 206-233 · Zbl 0232.47070
[35] Sadovskii, B.N, On a fixed point principle, Functional analysis appl., 1, 74-76, (1967) · Zbl 0165.49102
[36] Thompson, R.B, A unified approach to local and global fixed point indices, Advances in math., 3, 1-72, (1969) · Zbl 0186.57001
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.