Fixed point theorems for multivalued approximable mappings
Author:
P. S. Milojević
Journal:
Proc. Amer. Math. Soc. 73 (1979), 6572
MSC:
Primary 47H10
MathSciNet review:
512060
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Abstract: In this paper we introduce several classes of multivalued approximable mappings and develop the fixed point theory for these mappings acting in a cone. As an important special case we have the theory of kballcontractive perturbations of strongly pseudocontractive and accretive mappings.
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 D. G. de Figueiredo, Fixed point theorems for nonlinear operators and Galerkin approximations, J. Differential Equations 3 (1967), 271281. MR 0206761 (34:6578)
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 G. M. Gončarov, On some existence theorems for the solutions of a class of nonlinear operator equations, Math. Notes 7 (1970), 137141.
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 J. D. Hamilton, Noncompact mappings and cones in Banach spaces, Arch. Rational Mech. Anal. 48 (1972), 153162. MR 0341205 (49:5955)
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 M. Lees and M. H. Shultz, A LeraySchauder principle for Acompact mappings and the numerical solution of nonlinear twopoint boundary value problems, Numerical Solutions of Nonlinear Differential Equations (Proc. Adv. Sympos., Madison, Wis., 1966), Wiley, New York, 1966, pp. 167179. MR 0209924 (35:819)
 [7]
 P. S. Milojević, Multivalued mappings of Aproper and condensing type and boundary value problems, Ph.D. Thesis, Rutgers Univ., New Brunswick, N.J. (May 1975).
 [8]
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 [9]
 P. S. Milojević and W. V. Petryshyn, Continuation theorems and the approximationsolvability of equations involving multivalued Aproper mappings, J. Math. Anal. Appl. (3) 60 (1977), 658692. MR 0454760 (56:13008)
 [10]
 W. V. Petryshyn, Iterative construction of fixed points of contractive type mappings in Banach spaces, Numerical Analysis of Partial Differential Equations (C.I.M.E. 2 Ciclo, Ispra 1967), Edizioni Cremonese, Rome, 1968, pp. 307339. MR 0250435 (40:3674)
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 , On nonlinear Pcompact operators in Banach spaces with applications to constructive fixedpoint theorems, J. Math. Anal. Appl. 15 (1966), 228242. MR 0202014 (34:1890)
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 , On the approximationsolvability of equations involving Aproper and pseudoAproper mappings, Bull. Amer. Math. Soc. 81 (1975), 223312. MR 0388173 (52:9010)
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 W. V. Petryshyn and T. S. Tucker, On the functional equations involving nonlinear generalized Pcompact operators, Trans. Amer. Math. Soc. 135 (1969), 343373. MR 0247539 (40:804)
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 F. E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math., vol. 18, part 2, Amer. Math. Soc., Providence, R.I., 1976. MR 0405188 (53:8982)
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 P. S. Milojević, On the solvability and continuation type results for nonlinear equations with applications. I, Proc. Third Internat. Sympos. Topology and Appl., Belgrade, 1977.
 [16]
 , Fredholm alternatives and surjectivity results for multivalued Aproper and condensing mappings with applications to nonlinear integral and differential equations (submitted).
 [17]
 R. D. Nussbaum, Periodic solutions of some nonlinear autonomous functional differential equations. II, J. Differential Equations 14 (1973), 360394. MR 0372370 (51:8586)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197905120607
PII:
S 00029939(1979)05120607
Keywords:
Acompact,
Pcompact,
approximation solvability
Article copyright:
© Copyright 1979
American Mathematical Society
