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Petryshyn, W. V.

A new fixed point theorem and its application. (English) Zbl 0231.47030

Bull. Am. Math. Soc. 78, 225-229 (1972).
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Cited in 1 Review
Cited in 9 Documents

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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References:

[1] M. Altman, A fixed point theorem in Hilbert space, Bull. Acad. Polon. Sci. Cl. III. 5 (1957), 19 – 22, III (English, with Russian summary). · Zbl 0077.31902
[2] L. P. Belluce and W. A. Kirk, Fixed-point theorems for certain classes of nonexpansive mappings, Proc. Amer. Math. Soc. 20 (1969), 141 – 146. · Zbl 0165.16801
[3] Felix E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041 – 1044. · Zbl 0128.35801
[4] Felix E. Browder, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660 – 665. · Zbl 0164.44801
[5] Gabriele Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padova 24 (1955), 84 – 92 (Italian). · Zbl 0064.35704
[6] 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
[7] Dietrich Göhde, Zum Prinzip der kontraktiven Abbildung, Math. Nachr. 30 (1965), 251 – 258 (German). · Zbl 0127.08005 · doi:10.1002/mana.19650300312
[8] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004 – 1006. · Zbl 0141.32402 · doi:10.2307/2313345
[9] M. A. Krasnosel\(^{\prime}\)skiĭ, Two remarks on the method of successive approximations, Uspehi Mat. Nauk (N.S.) 10 (1955), no. 1(63), 123 – 127 (Russian).
[10] R. D. Nussbaum, The fixed point index and fixed point theorems for k-set-contractions, Ph.D. Thesis, University of Chicago, Chicago, Ill., 1969. · Zbl 0174.45402
[11] Roger D. Nussbaum, The fixed point index for local condensing maps, Ann. Mat. Pura Appl. (4) 89 (1971), 217 – 258. · Zbl 0226.47031 · doi:10.1007/BF02414948
[12] W. V. Petryshyn, Structure of the fixed points sets of \?-set-contractions, Arch. Rational Mech. Anal. 40 (1970/1971), 312 – 328. · Zbl 0218.47028 · doi:10.1007/BF00252680
[13] W. V. Petryshyn, Note on the structure of fixed point sets of 1-set-contractions, Proc. Amer. Math. Soc. 31 (1972), 189 – 194. · Zbl 0231.47031
[14] W. V. Petryshyn, Fixed point theorems for various classes of 1-set-contractive and 1-ball- contractive mappings in Banach spaces (in preparation). · Zbl 0277.47033
[15] Erich Rothe, Zur Theorie der topologischen Ordnung und der Vektorfelder in Banachschen Räumen, Compositio Math. 5 (1938), 177 – 197 (German). · Zbl 0018.13304
[16] B. N. Sadovskiĭ, On a fixed point principle, Funkcional. Anal. i Priložen. 1 (1967), no. 2, 74 – 76 (Russian). · Zbl 0165.49102
[17] J. Schauder, Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180. · JFM 56.0355.01
[18] J. R. L. Webb, Remarks on \?-set contractions, Boll. Un. Mat. Ital. (4) 4 (1971), 614 – 629 (English, with Italian summary). · Zbl 0219.47058
[19] P. P. Zabreĭko and M. A. Krasnosel\(^{\prime}\)skiĭ, A way of obtaining new fixed-point principles, Dokl. Akad. Nauk SSSR 176 (1967), 1233 – 1235 (Russian).
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