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Bulletin of the American Mathematical Society
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On the approximation-solvability of equations involving $A$-proper and pseudo-$A$-proper mappings

Author(s): W. V. Petryshyn
Journal: Bull. Amer. Math. Soc. 81 (1975), 223-312.
MSC (1970): Primary 47A15, 47H10; Secondary 39A40
MathSciNet review: 0388173
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References:

1.
S. Agmon, Lectures on elliptic boundary value problems, Van Nostrand Math. Studies, no. 2, Van Nostrand, Princeton, N.J., 1965. MR 31 #2504. MR 178246
2.
M. Š. Al'tman, A fixed point theorem in Banach space, Bull. Acad. Polon. Sci. Cl. III 5 (1957), 89-92. MR 19, 297. MR 87063
3.
M. Š. Al'tman, A fixed point theorem in Hilbert space, Bull. Acad. Polon. Sci. Cl. III 5 (1957), 19-22. MR 19, 297. MR 87064
4.
H. Amann, Fixed points of asymptotically linear maps in ordered Banach spaces, J. Functional Analysis 14 (1973), 162-171. MR 350527
5.
J.-P. Aubin, Approximation of elliptic boundary-value problems, Wiley, New York, 1972. MR 478662
6.
L. P. Belluce and W. A. Kirk, Fixed-point theorems for certain classes of nonexpansive mappings, Proc. Amer. Math. Soc. 20 (1969), 141-146. MR 38 #1663. MR 233341
7.
Ju. G. Borisovič and Ju. I. Sapronov, A contribution to the topological theory of condensing operators, Dokl. Akad. Nauk SSSR 183 (1968), 18-20=Soviet Math. Dokl. 9 (1968), 1304-1307. MR 38 #6414. MR 238138
8.
H. R. Brezis, Équations et inéquations non-linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble) 18 (1968), fasc. 1, 115-175. MR 42 #5113. MR 270222
9.
H. R. Brezis and M. Sibony, Méthodes d'approximation et d'itération pour les opérateurs monotones, Arch. Rational Mech. Anal. 28 (1967/68), 59-82. MR 36 #3177. MR 220110
10.
F. E. Browder, The solvability of non-linear functional equations, Duke Math. J. 30 (1963), 557-566. MR 27 #6133. MR 156204
11.
F. E. Browder, Mapping theorems for noncompact nonlinear operators in Banach spaces, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 337-342. MR 31 #5113. MR 180883
12.
F. E. Browder, Fixed point theorems for nonlinear semicontractive mappings in Banach spaces, Arch. Rational Mech. Anal. 21 (1965/66), 259-269. MR 34 #641. MR 200753
13.
F. E. Browder, Approximation-solvability of nonlinear functional equations in normed linear spaces, Arch. Rational Mech. Anal. 26 (1967), 33-42. MR 36 #3185. MR 220119
14.
F. E. Browder, Existence theorems for nonlinear partial differential equations, Proc. Sympos. Pure Math., vol. 16, Amer. Math. Soc., Providence, R.I., 1970, pp. 1-60. MR 42 #4855. MR 269962
15.
F. E. Browder, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660-665. MR 37 #5742. MR 230179
16.
F. E. Browder, Nonlinear elliptic boundary value problems and the generalized topological degree, Bull. Amer. Math. Soc. 76 (1970), 999-1005. MR 41 #8818. MR 264222
17.
F. E. Browder, Nonlinear mappings of analytic type in Banach spaces, Math. Ann. 185 (1970), 259-278. MR 41 #4318. MR 259683
18.
F. E. Browder, Normal solvability and $ø$-accretive mappings of Banach spaces, Bull. Amer. Math. Soc. 78 (1972), 186-192. MR 46 #6113. MR 306992
19.
F. E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math., vol. 18, part II, Amer. Math. Soc., Providence, R.I., (to appear). MR 405188
20.
F. E. Browder, Topology and nonlinear functional equations, Studia Math. 31 (1969), 189-204. MR 238134
21.
F. E. Browder, Remarks on nonlinear functional equations. III, Illinois J. Math. 9 (1965), 617-622. MR 32 #2941. MR 185474
22.
F. E. Browder and D. G. de Figueiredo, J-monotone nonlinear operators in Banach spaces, Nederl. Akad. Wetensch. Proc. Ser. A 69=Indag. Math. 28 (1966), 412-420. MR 34 #4957. MR 205122
23.
F. E. Browder and R. D. Nussbaum, The topological degree for noncompact nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 671-676. MR 38 #583. MR 232257
24.
F. E. Browder and W. V. Petryshyn, Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces, J. Functional Analysis 3 (1969), 217-245. MR 39 #6126. MR 244812
25.
F. E. Browder and W. V. Petryshyn, The topological degree and Galerkin approximations for noncompact operators in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 641-646. MR 37 #4678. MR 229100
26.
L. Cesari, Functional analysis and Galerkin's method, Michigan Math. J. 11 (1964), 385-414. MR 30 #4047. MR 173839
27.
J. Cronin-Scanlon, Analytic functional mappings, Ann. of Math. (2) 58 (1953), 175-181. MR 15, 234. MR 57464
28.
J. Cronin-Scanlon, Fixed points and topological degree in nonlinear analysis, Math. Surveys, no. 11, Amer. Math. Soc., Providence, R.I., 1964. MR 29 #1400. MR 164101
29.
J. Cronin-Scanlon, A definition of degree for certain mappings in Hilbert space, Amer. J. Math. 73 (1951), 763-772. MR 13, 662. MR 45953
30.
K. Deimling, Fixed points of generalized P-compact operators, Math. Z. 115 (1970), 188-196. MR 41 #9073. MR 264480
31.
L. Dozo, Opérateurs non-expansifs, P-compacts et propriétés géométriques de la norme, Doctoral Thesis, Université Libre de Bruxelles, 1969-1970.
32.
A. V. Džiškariani, The least square and Bubnov-Galerkin methods, Ž. Vyčisl. Mat. i Mat. Fiz. 8 (1968), 1110-1116. (Russian) MR 38 #6418. MR 238142
33.
A. V. Džiškariani, On the stability of approximation methods of the variational type, Ž. Vyčisl. Mat. i Mat. Fiz. 11 (1971), 569-579. (Russian). MR 477819
34.
D.E. Edmunds and J. R. L. Webb, A Leray-Schauder theorem for a class of nonlinear operators, Math. Ann. 182 (1969), 207-212. MR 40 #7895. MR 254688
35.
D. G. de Figueiredo, Topics in nonlinear functional analysis, Lecture Series, no. 48, University of Maryland, College Park, Md., 1967.
36.
D. G. de Figueiredo, Fixed-point theorems for nonlinear operators and Galerkin approximations, J. Differential Equations 3 (1967), 271-281. MR 34 #6578. MR 206761
37.
D. G. de Figueiredo and C. P. Gupta, Solvability of nonlinear equations of Hammerstein type (to appear).
38.
P. M. Fitzpatrick, A generalized degree for uniform limits of A-proper mappings, J. Math. Anal. Appl. 35 (1971), 536-552. MR 43 #6788. MR 281069
39.
P. M. Fitzpatrick, A-proper mappings and their uniform limits, Ph.D. Thesis, Rutgers University, New Brunswick, N. J., 1971. MR 303375
40.
P. M. Fitzpatrick, A-proper mappings and their uniform limits, Bull. Amer. Math. Soc. 78 (1972), 806-809. MR 46 #2512. MR 303375
41.
P. M. Fitzpatrick, Surjectivity results for nonlinear mappings from a Banach space to its dual, Math. Ann. 204 (1973), 177-188. MR 637098
42.
P. M. Fitzpatrick, On the structure of the set of solutions of equations involving A-proper mappings, Trans. Amer. Math. Soc. 189 (1974), 107-131. MR 336475
43.
K. O. Friedrichs, Spektraltheorie halbeschränkter Operatoren, Math. Ann. 109 (1934), 465-487, 685-713.
44.
S. Fučík, Fredholm alternative for nonlinear operators in Banach spaces and its applications to differential and integral equations, Časopis Pěst. Mat. 96 (1971), 371-390. MR 326502
45.
S. Fučík and J. Nečas, On the existence of Schauder bases in Sobolev spaces, Comment. Math. Univ. Carolinae 13 (1972), 163-175. MR 306890
46.
G. M. Gončarov, On some existence theorems for the solutions of a class of nonlinear operator equations, Mat. Zametki 7 (1970), 229-237=Math. Notes 7 (1970), 137-141. MR 41 #7499. MR 262894
47.
S. Granas, On a class of nonlinear mappings in Banach spaces, Bull. Acad. Polon. Sci. Cl. III 5 (1957), 867-871. (Russian) MR 19, 968.
48.
S. Granas, Introduction to topology of functional spaces, University of Chicago Lecture Notes, 1961.
49.
R. D. Grigorieff, Zur Theorie linearer approximations regularer Operatoren. I, II, Math. Nachr. (Erscheint).
50.
R. D. Grigorieff, Vereallgemeinerte approximativ kompakte Operatoren, Habilitationsschrift, Frankfurt, 1969.
51.
R. D. Grigorieff, Über die Fredholm-Alternative bei linearen approximations regularen Operatoren, Appl. Anal. 2 (1972), 217-227. MR 402521
52.
J. D. Hamilton, Noncompact mappings and cones in Banach spaces, Arch. Rational Mech. Anal. 48 (1972), 153-162. MR 341205
53.
P. Hess, On the Fredholm alternative for nonlinear functional equations in Banach spaces, Proc. Amer. Math. Soc. 33 (1972), 55-61. MR 301585
54.
P. Hess, on nonlinear mappings of monotone type homotopic to odd operators, J. Functional Analysis 11 (1972), 138-167. MR 350525
55.
S. Hildebrandt and E. Weinholtz, Constructive proofs of representation theorems in separable Hilbert space, Comm. Pure Appl. Math. 17 (1964), 369-373. MR 29 #3881. MR 166608
56.
H. Jeggle, Über die Approximation von linearen Gleichungen zweiter Art und Eigenwertproblemen in Banachschen Räumen, Math. Z. (Erscheint). MR 305114
57.
R. I. Kačurovskiĭ, Nonlinear monotone operators in Banach spaces, Uspehi Mat. Nauk 23 (1968), no. 2 (140), 121-168=Russian Math. Surveys 23 (1968), no. 2, 117-165. MR 37 #2045. MR 226455
58.
R. I. Kačurovskiĭ, On the Fredholm theory for nonlinear operator equations, Dokl. Akad. Nauk SSSR 192 (1970), 969-972=Soviet Math. Dokl. 11 (1970), 751-754. MR 42 #911. MR 266002
59.
R. I. Kačurovskiĭ, On nonlinear operators whose ranges are subspaces, Dokl. Akad. Nauk SSSR 196 (1971), 508-51l =Soviet Math. Dokl. 12 (1971), 168-172. MR 477916
60.
R. I. Kačurovskiĭ, Approximate methods for the solution of nonlinear operator equations, Izv. Vysš. Učebn. Zaved. Matematika 1967, no. 12 (67), 27-37. (Russian) MR 37 #2044. MR 226454
61.
R. I. Kačurovskiĭ, Tihonov's fixed-point principle and equations with operators weakly closed on a kernel, Dokl. Akad. Nauk SSSR 183 (1968), 517-520=Soviet Math. Dokl. 9 (1968), 1411-1414. MR 38 #5082. MR 236788
62.
S. Kaniel, Quasi-compact non-linear operators in Banach space and applications, Arch. Rational Mech. Anal. 20 (1965), 259-278. MR 32 #4575. MR 187121
63.
L. V. Kantorovič, Functional analysis and applied mathematics, Uspehi Mat. Nauk 3 (1948), no. 6 (28), 89-185; English transl., Nat. Bur. Standards Rep., no. 1509, U.S. Dept. of Commerce, Nat. Bur. Standards, Washington, D.C., 1952. MR 10, 380; 14, 766. MR 53389
64.
T. Kato, Perturbation theory for linear operators, Die Grundlehren der math. Wissenschaften, Band 132, Springer-Verlag, New York, 1966. MR 34 #3324. MR 203473
65.
W. A. Kirk, Mappings of generalized contractive type, J. Math. Anal. Appl. 32 (1970), 567-572. MR 42 #6675. MR 271794
66.
W. A. Kirk, On nonlinear mappings of strongly semicontractive type, J. Math. Anal. Appl. 27 (1969), 409-412. MR 39 #6128. MR 244814
67.
M. A. Krasnosel'skiĭ, Topological methods in the theory of nonlinear integral equations, GITTL, Moscow, 1956; English transl., Macmillan, New York, 1964. MR 20 #3464; 28 #2414. MR 159197
68.
M. A. Krasnosel'skiĭ, Two remarks on the method of successive approximations, Uspehi Mat. Nauk 10 (1955), no. 1 (63), 123-127. (Russian) MR 16, 833. MR 68119
69.
M. A. Krasnosel'skiĭ, Convergence of Galerkin's method for nonlinear equations, Dokl. Akad. Nauk SSSR 73 (1950), 1121-1124. (Russian) MR 12, 187. MR 36937
70.
M. A. Krasnosel'skiĭ, Positive solutions to operator equations, Fizmatgiz, Moscow, 1962; English transl., Noordhoff, Groningen, 1964. MR 26 #2862; 31 #6107. MR 181881
71.
M. A. Krasnosel'skiĭ and P. E. Sobolevskiĭ, Structure of the set of solutions of an equation of parabolic type, Ukrain. Mat. Ž. 16 (1964), 319-333; English transl., Amer. Math. Soc. Transl. (2) 51 (1966), 113-131. MR 29 #3763. MR 166488
72.
M. A. Krasnosel'skiĭ, G. M. Vaĭnikko, P. P. Zabreĭko, Ja. B. Rutickiĭ and V. Ja. Stecenko, Approximate solution of operator equations, "Nauka", Moscow, 1969; English transl., Wolters-Noordhoff, Groningen, 1972. MR 41 #4271. MR 385655
73.
M. Kravčuk, Application of the method of moments to the solution of linear differential and integral equations, Ukrain. Akad. Nauk. Kiev, 1936.
74.
O. L. Ladyženskaja, On integral estimates, convergence, approximate methods, and solution in functionals for elliptic equations, Vestnik Leningrad. Univ. 13 (1958), no. 7, 60-69. (Russian) MR 20 #5353. MR 98903
75.
A. D. Ljaško, The convergence of Galerkin type methods, Dokl. Akad. Nauk SSSR 120 (1958), 242-244. (Russian) MR 20 #4346. MR 97882
76.
P. D. Lax and A. N. Milgram, Parabolic equations, Contributions to the Theory of Partial Differential Equations, Ann. of Math. Studies, no. 33, Princeton Univ. Press, Princeton, N.J., 1954, pp. 167-190. MR 16, 709. MR 67317
77.
M. Lees and M. H. Schultz, A Leray-Schauder principle for A-compact mappings and the numerical solution of non-linear two-point boundary value problems, Numerical Solutions of Nonlinear Differential Equations (Proc. Adv. Sympos., Madison, Wis., 1966), Wiley, New York, 1966, pp. 167-179. MR 35 #819. MR 209924
78.
J. Leray, Topologie des espaces abstraits de M. Banach, C.R. Acad. Sci. Paris 200 (1935), 1082-1084.
79.
J. Leray and J.-P. Lions, Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France 93 (1965), 97-107. MR 33 #2939. MR 194733
80.
J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. École Norm. Sup. 51 (1934), 45-78. MR 1509338
81.
J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod; Gauthier-Villars, Paris, 1969. MR 41 #4326. MR 259693
82.
A. Ju. Lučka, The rate of convergence of certain projection methods for linear operator equations, Ukrain. Mat. Ž. 23 1971), 307-317. (Russian) MR 44 #2054. MR 284830
83.
J. T. Marti, Introduction to the theory of bases, Springer Tracts in Natural Philosophy, vol. 18, Springer-Verlag, Berlin and New York, 1970. MR 438075
84.
A. E. Martynjuk, Variational methods in boundary value problems for weakly elliptic equations, Dokl. Akad. Nauk SSSR 126 (1959), 1222-1225. (Russian) MR 22 #4867. MR 114037
85.
V. A. Medvedev, On the convergence of the Bubnov-Galerkin method, Prikl. Mat. Meh. 27 (1963), 1148-1151 =J. Appl. Math. Mech.27 (1963), 1769-1774. MR 29 #1753. MR 164456
86.
S. G. Mihlin, Variational methods in mathematical physics, GITTL, Moscow, 1957; German transl., Akademie-Verlag, Berlin, 1962; English transl., Macmillan, New York, 1964. MR 22 #1981; 25 #4658; 30 #2712. MR 172493
87.
S. G. Mihlin, On the convergence of Galerkin's method, Dokl. Akad. Nauk SSSR 61 (1948), 197-199. (Russian) MR 10, 129. MR 26253
88.
S. G. Mihlin, The numerical performance of variational methods, "Nauka", Moscow, 1966; Wolters-Noordhoff, Groningen, 1971. MR 34 #3747; 43 #4236. MR 278506
89.
G. J. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962), 341-346. MR 29 #6319. MR 169064
90.
G. J. Minty, On a "monotonicity" method for the solution of nonlinear equations in Banach spaces, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 1038-1041. MR 28 #5358. MR 162159
91.
J. Nečas, Remark on the Fredholm alternative for nonlinear operators with application to nonlinear integral equations of generalized Hammerstein type, Comment. Math. Univ. Carolinae 13 (1972), 109-120. MR 46 #4301. MR 305171
92.
J. Nečas, Fredholm alternative for nonlinear operators and applications to partial differential equations and integral equations, Časopis Pěst. Mat. 97 (1972), 65-71, 94. MR 46 #7994. MR 308882
93.
R. D. Nussbaum, The fixed point index and fixed point theorems for k-set-contractions, Ph.D. Dissertation, University of Chicago, Chicago, Ill., 1969.
94.
R. D. Nussbaum, The radius of the essential spectrum, Duke Math. J. 37 (1970), 473-478. MR 41 #9028. MR 264434
95.
R. D. Nussbaum, The fixed point index for local condensing maps, Ann. Mat. Pura Appl. (4) 89 (1971), 217-258. MR 47 #903. MR 312341
96.
R. D. Nussbaum, The ball intersection property for Banach spaces, Notices Amer. Math. Soc. 17 (1970), 1073. MR 308744
97.
T. O'Neil and J. W. Thomas, On the equivalence of multiplicity and the generalized topological degree, Trans. Amer. Math. Soc. 167 (1972), 333-345. MR 45 #7555. MR 298503
98.
D. Pascali, Operatori nelineari, Acad. Rep. Soc. Romania, Bucarest, 1964.
99.
G. I. Petrov, Application of the Galerkin method to the stability problem of viscous fluid, Appl. Math. Mech. 3 (1940).
100.
W. Petry, Existence theorems for a class of nonlinear operator equations, J. Math. Anal. Appl. 43 (1973), 250-260. MR 344958
101.
W. Petry, Iterative Lösung gewisser nichtlinearer Operator-gleichungen mit Anwendung auf quasilineare Differentialgleichungen, Aequationes Math. 8 (1972), 113-135. MR 46 #6585. MR 307465
102.
W. V. Petryshyn, Direct and iterative methods for the solution of linear operator equations in Hilbert space, Trans. Amer. Math. Soc. 105 (1962), 136-175. MR 26 #3180. MR 145651
103.
W. V. Petryshyn, Constructional proof of Lax-Milgram lemma and its application to non-K-p.d. abstract and differential operator equations, J. Soc. Indust. Appl. Math. Ser. B. Numer. Anal. 2 (1965), 404-420. MR 33 #1764. MR 193544
104.
W. V. Petryshyn, On a class of K-p.d. ad non-K-p.d. operators and operator equations, J. Math. Anal. Appl. 10 (1965), 1-24. MR 35 #7141. MR 216306
105.
W. V. Petryshyn, On the extension and the solution of nonlinear operator equations, Illinois J. Math. 10 (1966), 255-274. MR 34 #8242. MR 208432
106.
W. V. Petryshyn, Further remarks on nonlinear P-compact operators in Banach spaces, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 684-687; see also: J. Math. Anal. Appl. 16 (1966), 243-253. MR33 #3148; #6458. MR 198299
107.
W. V. Petryshyn, On a fixed point theorem for nonlinear P-compact operators in Banach space, Bull. Amer. Math. Soc. 72 (1966), 329-334. MR 33 #1768. MR 193548
108.
W. V. Petryshyn, On nonlinear P-compact operators in Banach space with applications to constructive fixed-point theorems, J. Math. Anal. Appl. 15 (1966), 228-242. MR 34 #1890. MR 202014
109.
W. V. Petryshyn, Projection methods in nonlinear numerical functional analysis, J. Math. Mech. 17 (1967), 353-372. MR 36 #2025. MR 218941
110.
W. V. Petryshyn, Remarks on the approximation-solvability of nonlinear functional equations, Arch. Rational Mech. Anal. 26 (1967), 43-49. MR 36 #3186. MR 220120
111.
W. V. Petryshyn, Iterative construction of fixèd points of contractive type mappings in Banach spaces, Numerical Analysis of Partial Differential Equations (C.I.M.E. 2o Ciclo, Ispra, 1967), Edizioni Cremonese, Rome, 1968, pp. 307-339. MR 40 #3674. MR 250435
112.
W. V. Petryshyn, On the approximation-solvability of nonlinear equations, Math. Ann. 177 (1968), 156-164. MR 37 #2048. MR 226458
113.
W. V. Petryshyn, On projectional-solvability and the Fredholm alternative for equations involving linear A-proper operators, Arch. Rational Mech. Anal. 30 (1968), 270-284. MR 37 #6776. MR 231221
114.
W. V. Petryshyn, Fixed-point theorems involving P-compact, semicontractive, and accretive operators not defined on all of a Banach space, J. Math. Anal. Appl. 23 (1968), 336-354. MR 38 #588. MR 232262
115.
W. V. Petryshyn, Nonlinear equations involving noncompact operators, Proc. Sympos. Pure Math., vol. 18, part 1, Amer. Math. Soc., Providence, R.I., 1970, pp. 206-233. MR 42 #6670. MR 271789
116.
W. V. Petryshyn, Some examples concerning the distinctive features of bounded linear A-proper mappings and Fredholm mappings, Arch. Rational Mech. Anal. 33 (1969), 331-338. MR 39 #3331. MR 241996
117.
W. V. Petryshyn, Invariance of domain theorem for locally A-proper mappings and its implications, J. Functional Analysis 5 (1970), 137-159. MR 42 #914. MR 266005
118.
W. V. Petryshyn, On existence theorems for nonlinear equations involving noncompact mappings, Proc. Nat. Acad. Sci. U.S.A. 67 (1970), 326-330. MR 42 #3631. MR 268734
119.
W. V. Petryshyn, Antipodes theorem for A-proper mappings and its applications to mappings of the modified type (S) or (S), J. Functional Analysis 7 (1971), 165-211. MR 435963
120.
W. V. Petryshyn, Surjectivity theorems for odd maps of A-proper type, Math. Ann. 192 (1971), 155-172. MR 45 #999. MR 291911
121.
W. V. Petryshyn, On nonlinear equations involving pseudo-A-proper mappings and their uniform limits with applications, J. Math. Anal. Appl. 38 (1972), 672-720. MR 326519
122.
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. MR 328688
123.
W. V. Petryshyn, Fredholm alternative for nonlinear A-proper mappings with applications to nonlinear elliptic boundary value problems, J. Functional Analysis (to appear). MR 361963
124.
W. V. Petryshyn, Stability theory for linear A-proper mappings, Proc. Math.-Phys. Sec. Ševčenko Sci. Soc., 1973.
125.
W. V. Petryshyn, On the relationship of A-properness to mappings of monotone type (in preparation).
126.
W. V. Petryshyn, Fredholm alternative for nonlinear k-ball-contractive mappings with applications, J. Differential Equations (to appear). MR 355713
127.
W. V. Petryshyn and P. M. Fitzpatrick, On 1-set and 1-ball contractions with applications to perturbation problems for non-linear bijective maps and linear Fredholm maps, Boll. Un. Mat. Ital. (4) 7 (1973), 102-124. MR 343114
128.
W. V. Petryshyn and P. M. Fitzpatrick, A degree theory, fixed point theorems, and mappings theorems for multivalued and noncompact mappings, Trans. Amer. Math. Soc. 194 (1974), 1-25.
129.
W. V. Petryshyn and T. S. Tucker, On the functional equations involving nonlinear generalized P-compact operators, Trans. Amer. Math. Soc. 135 (1969), 343-373. MR 40 #804. MR 247539
130.
S. I. Pohožaev, The solvability of nonlinear equations with odd operators, Funkcional. Anal. i Priložen. 1 (1967), no. 3, 66-73. (Russian) MR 36 #4396. MR 221344
131.
N. I. Pol'skiĭ, Projective methods in applied mathematics, Dokl. Akad. Nauk SSSR 143 (1962), 787-790=Soviet Math. Dokl. 3 (1962), 488-491. MR 26 #3173. MR 145644
132.
N. I. Pol'skiĭ, On the convergence of certain approximate methods of analysis, Ukrain. Mat. Ž. 7 (1955), 56-70. (Russian) MR 17, 64. MR 70978
133.
A. J. B. Potter, Non-linear A-proper mappings of the analytic type, Canad. J. Math. 25 (1973), 468-474. MR 47 #5666. MR 317118
134.
R. T. Rockafellar, Local boundedness of nonlinear, monotone operators, Michigan Math. J. 16 (1969), 397-407. MR 40 #6229. MR 253014
135.
E. Rothe, Zur Theorie der topologischen Ordnung und der Vektorfelder in Banachschen Räumen, Compositio Mat. 5 (1937), 177-197.
136.
B. N. Sadovskiĭ, Ultimately compact and condensing mappings, Uspehi Mat. Nauk 27 (1972), 81-146. (Russian). MR 428132
137.
J. Schauder, Invarianz des Gebietes in Funktionalräumen, Studia Math. 1 (1929), 123-139.
138.
J. Schauder, Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180.
139.
J. T. Schwartz, Compact analytic mappings of B-spaces and a theorem of Jane Cronin, Comm. Pure Appl. Math. 16 (1963), 253-260. MR 29 #481. MR 163178
140.
M. Shinbrot, A fixed point theorem, and some applications, Arch. Rational Mech. Anal. 19 (1964), 255-271. MR 29 #6323. MR 169068
141.
V. M. Šalov, Minimum principle of a quadratic functional for a hyperbolic equation, Differencial'nye Uravnenija 1 (1965), 1338-1365. (Russian) MR 32 #4405. MR 186950
142.
I. V. Skripnik, Nonlinear elliptic equations of higher order, "Naukova Dumka", Kiev, 1973. MR 355330
143.
P. E. Sobolevskiĭ, On equations with operators forming an acute angle, Dokl. Akad. Nauk SSSR 116 (1957), 754-757. MR 20 #4194. MR 97727
144.
C. A. Stuart, The fixed point index of a differentiable (β) k-set contraction, J. London Math. Soc. (2) 5 (1972), 691-696. MR 47 #907. MR 312345
145.
F. Stummel, Approximation methods in analysis, Lecture Notes Series, no. 35, Aarhus Universitet, 1973. MR 468102
146.
T. S. Tucker, Leray-Schauder theorem for P-compact operators and its consequences, J. Math. Anal. Appl. 23 (1968), 355-364. MR 37 #6805. MR 231250
147.
M. M. Vaĭnberg, Variational methods for the study of non-linear operators, GITTL, Moscow, 1956; English transl., Holden-Day, San Francisco, Calif., 1964. MR 19, 567; 31 #638.
148.
G. Vaĭnikko, On the convergence of the collocation method for nonlinear differential equations, Ž. Vyčisl. Mat. i Mat. Fiz. 6 (1966), no. 1, 35-42. (Russian) MR 33 #5129. MR 196945
149.
G. Vaĭnikko, A perturbed Galerkin method and the general theory of approximate methods for nonlinear equations, Ž. Vyčisl. Mat. i Mat. Fiz. 7 (1967), 723-751. (Russian) MR 36 #1095. MR 218006
150.
G. Vaĭnikko, Necessary and sufficient conditions for stability of the Galerkin-Petrov method, Tartu Riikl. Ül. Toimetised Vih. 177 (1965), 141-147. (Russian) MR 36 #1093. MR 218004
151.
G. N. Vaĭnikko and B. N. Sadovskiĭ, The rotation of condensing vector fields, Problemy Mat. Anal. Slož. Sistem Vyp. 2 (1968), 84-88. (Russian) MR 45 #2546. MR 293469
152.
R. S. Varga, Functional analysis and approximation theory in numerical analysis, Conference Board of the Math. Sci. Regional Conf. Ser. in Appl. Math., no. 3, SIAM, Philadelphia, Pa., 1971. MR 46 #9602. MR 310504
153.
G. Vidossich, On Peano phenomenon, Boll. Un. Mat. Ital. (4) 3 (1970), 33-42. MR 42 #6674. MR 271793
154.
J. R. L. Webb, Fixed point theorems for non-linear semicontractive operators in Banach spaces, J. London Math. Soc. (2) 1 (1969), 683-688. MR 40 #3392. MR 250152
155.
J. R. L. Webb, Mapping and fixed-point theorems for nonlinear operators in Banach spaces, Proc. London Math. Soc. (3) 20 (1970), 451-468. MR 42 #917. MR 266008
156.
J. R. L. Webb, Remarks on k-set contractions, Boll. Un. Mat. Ital. (4) 4 (1971), 614-629. MR 45 #2544. MR 293467
157.
J. R. L. Webb, A fixed point theorem and applications to functional equations in Banach spaces, Boll. Un. Mat. Ital. (4) 4 (1971), 775-788. MR 377631
158.
H. Ship-fah Wong, Le dégrée topologique de certaines applications non-compactes, nonlinéaires, Ph.D. Dissertation, University of Montreal, 1970.
159.
H. Ship-fah Wong, The topological degree of A-proper maps, Canad. J. Math. 23 (1971), 403-412. MR 44 #5843. MR 288647
160.
H. Ship-fah Wong, A product formula for the degree of A-proper maps, J. Functional Analysis 10 (1972), 361-371. MR 345128
161.
S. Yamamuro, A note on d-ideals in some near-algebras, J. Austral. Math. Soc. 7 (1967), 129-134. MR 35 #3456. MR 212585
162.
G. N. Jaskova and M. N. Jakovlev, Some conditions for the stability of the Petrov-Galerkin method, Trudy Mat. Inst. Steklov. 66 (1962), 182-189. (Russian) MR 27 #5146. MR 155207
163.
E. Zarantonello, The closure of the numerical range contains the spectrum, Bull. Amer. Math. Soc. 70 (1964), 781-787. MR 30 #3389. MR 173176

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Additional Information:

DOI: 10.1090/S0002-9904-1975-13728-1
PII: S 0002-9904(1975)13728-1




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