Fixed point theorems for multivalued approximable mappings
HTML articles powered by AMS MathViewer
- by P. S. Milojević PDF
- Proc. Amer. Math. Soc. 73 (1979), 65-72 Request permission
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 k-ball-contractive perturbations of strongly pseudo-contractive and accretive mappings.References
- 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, DOI 10.1090/S0002-9947-1974-0336475-5
- P. M. Fitzpatrick and W. V. Petryshyn, Fixed point theorems and the fixed point index for multivalued mappings in cones, J. London Math. Soc. (2) 12 (1975/76), no. 1, 75–85. MR 405180, DOI 10.1112/jlms/s2-12.1.75
- Djairo Guedes de Figueiredo, Fixed-point theorems for nonlinear operators and Galerkin approximations, J. Differential Equations 3 (1967), 271–281. MR 206761, DOI 10.1016/0022-0396(67)90031-9 G. M. Gončarov, On some existence theorems for the solutions of a class of nonlinear operator equations, Math. Notes 7 (1970), 137-141.
- John David Hamilton, Noncompact mappings and cones in Banach spaces, Arch. Rational Mech. Anal. 48 (1972), 153–162. MR 341205, DOI 10.1007/BF00250430
- 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) John Wiley & Sons, Inc., New York, N.Y., 1966, pp. 167–179. MR 0209924 P. S. Milojević, Multivalued mappings of A-proper and condensing type and boundary value problems, Ph.D. Thesis, Rutgers Univ., New Brunswick, N.J. (May 1975).
- P. S. Milojević, A generalization of Leray-Schauder theorem and surjectivity results for multivalued $A$-proper and pseudo $A$-proper mappings, Nonlinear Anal. 1 (1976/77), no. 3, 263–276. MR 637079, DOI 10.1016/0362-546X(77)90035-9
- P. S. Milojević and W. V. Petryshyn, Continuation theorems and the approximation-solvability of equations involving multivalued $A$-proper mappings, J. Math. Anal. Appl. 60 (1977), no. 3, 658–692. MR 454760, DOI 10.1016/0022-247X(77)90007-5
- 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. 307–339. MR 0250435
- 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 202014, DOI 10.1016/0022-247X(66)90114-4
- W. V. Petryshyn, On the approximation-solvability of equations involving $A$-proper and psuedo-$A$-proper mappings, Bull. Amer. Math. Soc. 81 (1975), 223–312. MR 388173, DOI 10.1090/S0002-9904-1975-13728-1
- 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 247539, DOI 10.1090/S0002-9947-1969-0247539-7
- Felix E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1976, pp. 1–308. MR 0405188 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. —, Fredholm alternatives and surjectivity results for multivalued A-proper and condensing mappings with applications to nonlinear integral and differential equations (submitted).
- Roger D. Nussbaum, Periodic solutions of some nonlinear, autonomous functional differential equations. II, J. Differential Equations 14 (1973), 360–394. MR 372370, DOI 10.1016/0022-0396(73)90053-3
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 65-72
- MSC: Primary 47H10
- DOI: https://doi.org/10.1090/S0002-9939-1979-0512060-7
- MathSciNet review: 512060