The solution by iteration of nonlinear functional equations in Banach spaces

Browder, F. E.; Petryshyn, W. V.

doi:10.1090/S0002-9904-1966-11544-6

The solution by iteration of nonlinear functional equations in Banach spaces
HTML articles powered by AMS MathViewer

by F. E. Browder and W. V. Petryshyn PDF

Bull. Amer. Math. Soc. 72 (1966), 571-575

References

L. P. Belluce and W. A. Kirk, Fixed-point theorems for families of contraction mappings, Pacific J. Math. 18 (1966), 213–217. MR 199703, DOI 10.2140/pjm.1966.18.213
Felix E. Browder, On the iteration of transformations in noncompact minimal dynamical systems, Proc. Amer. Math. Soc. 9 (1958), 773–780. MR 96975, DOI 10.1090/S0002-9939-1958-0096975-9
Felix E. Browder, Existence of periodic solutions for nonlinear equations of evolution, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1100–1103. MR 177295, DOI 10.1073/pnas.53.5.1100
Felix E. Browder, Fixed-point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1272–1276. MR 178324, DOI 10.1073/pnas.53.6.1272
Felix E. Browder, Mapping theorems for noncompact nonlinear operators in Banach spaces, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 337–342. MR 180883, DOI 10.1073/pnas.54.2.337
Felix E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041–1044. MR 187120, DOI 10.1073/pnas.54.4.1041
Felix E. Browder, Fixed point theorems for nonlinear semicontractive mappings in Banach spaces, Arch. Rational Mech. Anal. 21 (1966), 259–269. MR 200753, DOI 10.1007/BF00282247
F. E. Browder and W. V. Petryshyn, The solution by iteration of linear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 566–570. MR 190744, DOI 10.1090/S0002-9904-1966-11543-4
W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004–1006. MR 189009, DOI 10.2307/2313345
M. A. Krasnosel′skiĭ, Two remarks on the method of successive approximations, Uspehi Mat. Nauk (N.S.) 10 (1955), no. 1(63), 123–127 (Russian). MR 0068119
Helmut Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math.-Verein. 59 (1957), no. Abt. 1, 131–140 (German). MR 84116

Additional Information

Journal: Bull. Amer. Math. Soc. 72 (1966), 571-575
DOI: https://doi.org/10.1090/S0002-9904-1966-11544-6
MathSciNet review: 0190745