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

The solution by iteration of nonlinear functional equations in Banach spaces. (English) Zbl 0138.08202

Bull. Am. Math. Soc. 72, 571-575 (1966).
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Cited in 170 Documents

Keywords:

functional analysis
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\textit{F. E. Browder} and \textit{W. V. Petryshyn}, Bull. Am. Math. Soc. 72, 571--575 (1966; Zbl 0138.08202)
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References:

[1] L. P. Belluce and W. A. Kirk, Fixed-point theorems for families of contraction mappings, Pacific J. Math. 18 (1966), 213 – 217. · Zbl 0149.10701
[2] Felix E. Browder, On the iteration of transformations in noncompact minimal dynamical systems, Proc. Amer. Math. Soc. 9 (1958), 773 – 780. · Zbl 0092.12602
[3] Felix E. Browder, Existence of periodic solutions for nonlinear equations of evolution, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1100 – 1103. · Zbl 0135.17601
[4] Felix E. Browder, Fixed-point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1272 – 1276. · Zbl 0125.35801
[5] Felix E. Browder, Mapping theorems for noncompact nonlinear operators in Banach spaces, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 337 – 342. · Zbl 0133.08101
[6] Felix E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041 – 1044. · Zbl 0128.35801
[7] Felix E. Browder, Fixed point theorems for nonlinear semicontractive mappings in Banach spaces, Arch. Rational Mech. Anal. 21 (1966), 259 – 269. · Zbl 0144.39101
[8] 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. , https://doi.org/10.1090/S0002-9904-1966-11543-4 F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 571 – 575. · Zbl 0138.08201
[9] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004 – 1006. · Zbl 0141.32402
[10] M. A. Krasnosel\(^{\prime}\)skiĭ, Two remarks on the method of successive approximations, Uspehi Mat. Nauk (N.S.) 10 (1955), no. 1(63), 123 – 127 (Russian).
[11] W. V. Petryshyn, On the construction of fixed points and solutions of nonlinear equations with demicompact mappings, (to appear). · Zbl 0138.39802
[12] Helmut Schaefer, Über die Methode sukzessiver Approximationen, Jber. Deutsch. Math. Verein. 59 (1957), no. Abt. 1, 131 – 140 (German). · Zbl 0077.11002
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