References
Aronszajn, N.: La correspondant topologique de l'unicite dans la theorie des equations differentielles. Ann of Math.43, 730–738 (1942).
Begle, E.: A fixed point theorem. Ann. of Math.51, 544–550 (1950).
Berge, C.: Espaces topologiques, fonctions multivoques. Paris: Dunod, 1959.
Browder, F.: Nonlinear operators and nonlinear equations of evolution in Banach spaces, to appear in Symposium on Nonlinear Functional Analysis, Amer. Math. Soc., Chicago 1968.
—— Local and global properties of nonlinear mappings in Banach spaces. Instituto Naz. di Alta Math., Symposia Math.11, 13–35 (1968).
—— On continuity of fixed point under deformations of continuous mappings. Summa Brasil Math.4, 183–190 (1960).
—— On the fixed point index for continuous mappings of locally connected spaces. Summa Brasil Math.4, 253–293 (1960).
—— The fixed point theory of multivalued mappings in topological vector spaces. Math. Ann.177, 283–301 (1968).
Browder, F., Nussbaum, R.: The topological degree for noncompact nonlinear mappings in Banach spaces. Bull. Amer. Math. Soc.74, 671–676 (1968).
Coddington, E., Levinson, N.: Theory of ordinary differential equations. New York: McGraw Hill, 1955.
Cronin, J.: Fixed points and topological degree in nonlinear analysis. Surveys Amer. Math. Soc.11 1964.
Deleanu, A.: Theorie des points fixes sur les retracts de voisinage des espaces convexoides. Bull. Soc. Math. France,87, 235–243 (1959).
Dold, A.: Fixed point index and fixed point theorem for euclidean neighborhood retracts. Topology4, 1–8 (1965).
Eilenberg, S., Montgomery, D.: Fixed point theorems for multivalued transformations. Amer. J. Math.68, 214–222 (1946).
Elworthy, K., Tromba, A.: Degree theory on Banach manifolds, Symposium on Nonlinear Functional Analysis. Amer. Math. Soc., Chicago, 1968.
Fadell, E.: On a coincidence theorem of F. B. Fuller. Pacific J. Math.15, 825–834 (1965).
—— Recent results in the fixed point theory of continuous maps. Bull. Amer. Math. Soc.76, 10–29 (1970).
Gabriel, P., Zisman, M.: Calculus of fractions and homotopy theory. Berlin-Heidelberg-New York: Springer 1967.
Granas, A.: Sur la notion du degre topologiques pour une certaine classe de transformations multivalentes dans les espaces de Banach. Bull. Acad. Polon. Sci.7, 191–194 (1959).
—— Theorem on antipodes and theorems on fixed points for a certain class of multivalued mappings in Banach spaces. Bull. Acad. Polon. Sci.7, 271–275 (1959).
-- Jaworowski, J.: Some theorems on multivalued mappings of subsets of the Euclidean space. Bull. Acad. Polon. Sci., u(1959), 277–283.
Halpern, B.: Algebraic topology and set valued maps, to appear.
-- Fixed point theorems for set valued maps in infinite dimensional spaces, to appear.
Jaworowski, J.: Some consequences of the Vietoris mapping theorem. Fund. Math.45, 261–272 (1957–58).
Kato, T.: Nonlinear semigroups and evolution equations. J. Math. Soc. Japan19, 508–520 (1967).
Klee, V.: Leray Schauder theory without local convexity. Math. Ann.141, 286–296 (1960).
Krasnoselskii, M.: Topological methods in the theory of nonlinear integral equations. New York: MacMillan, 1964.
Leray, J.: Sur les equations et les transformations. J. Math. Pures Appl.24, 201–248 (1945).
—— La théorie des points fixes et ses applications en analyse. Proc. Int. Math. Congress. Cambridge 1950, vol. 2, 202–208.
—— Théorie des points fixes: indice totale et nombre de Lefschetz. Bull. Soc. Math. Fr.87, 221–233 (1959).
Michael, E.: Continuous selections III. Ann. of Math.165, 375–390 (1957).
Mukherjea, K.: Fredholm structures and cohomology, thesis, Cornell, 1968.
Nagumo, M.: Degree of mapping in convex linear topological spaces. Amer. J. Math.73, 497–511 (1951).
Nakaoka, M.: Note on the Lefschetz fixed point theorem. Osaka J. Math.6, 135–142 (1969).
Nussbaum, R.: The fixed point index and asymptotic fixed point theorems fork-set contractions. Bull. Amer. Math. Soc.75, 490–495 (1969).
-- A geometric approach to the fixed point index, to appear.
O'Neill, B.: Induced homology homomorphisms for set valued maps. Pac. J. Math.7, 1179–1184 (1957).
Petryshyn, W.: Invariance of domain theorem for locallyA-proper mappings and its implications. J. Funct. Anal.5, 137–159 (1970).
—— Browder, F.: Approximation methods and the generalised topological degree for nonlinear mappings in Banach spaces. J. Funct. Anal.3, 217–245 (1969).
Powers, M. S.: Multivalued mappings and Lefschetz fixed point theorems, to appear.
Spanier, E.: Algebraic topology. New York: McGraw Hill, 1966.
Thompson, R.: A unified approach to local and global fixed point indices. Advances in Math.3, 1–71 (1969).
Van der Valt, T.: Fixed and almost fixed points. Amsterdam, Mathematical Centre Tracts, 1967.
Wolkowisky, J.: Nonlinear Hill's equation, in preparation.
—— Nonlinear Sturm-Liouville problems. Arch. Rat. Mech. Anal.35, 299–320 (1969).
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Calvert, B.D. The local fixed point index for multivalued transformations in a Banach space. Math. Ann. 190, 119–128 (1970). https://doi.org/10.1007/BF01431494
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DOI: https://doi.org/10.1007/BF01431494