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Extensions of some fixed point theorems of Rhoades. (English) Zbl 0524.47033


MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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References:

[1] Browder, F. E.; Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl., 20, 197-228 (1967) · Zbl 0153.45701
[2] Ciric, L. B., A Generalization of Banach’s contraction principle, (Proc. Amer. Math. Soc., 45 (1974)), 267-273 · Zbl 0291.54056
[3] Ciric, L. B., Quasi-contractions in Banach spaces, Publ. Inst. Math., 21, 41-48 (1977) · Zbl 0361.47020
[4] Hicks, Troy L.; Kubicek, J. D., On the Mann iteration process in Hilbert spaces, J. Math. Anal. Appl., 59, 498-504 (1977) · Zbl 0361.65057
[5] Huffman, E. W.; Hicks, Troy L., Fixed point theorems in generalized Hilbert spaces, J. Math. Anal. Appl., 64, 562-569 (1978) · Zbl 0405.47037
[6] Ishikawa, S., Fixed points by a new iteration method, (Proc. Amer. Math. Soc., 44 (1974)), 147-150 · Zbl 0286.47036
[7] Mann, W. R., Mean value methods in iteration, (Proc. Amer. Math. Soc., 4 (1953)), 506-510 · Zbl 0050.11603
[8] Opial, Z., Weak convergence of the sequence of successive approximations for nonex pansive mappings, Bull. Amer. Math. Soc., 73, 591-597 (1967) · Zbl 0179.19902
[9] Pal, T. K.; Maiti, M., Extensions of fixed point theorems of Rhoades and Ciric, (Proc. Amer. Math. Soc., 64 (1977)), 283-286 · Zbl 0335.47040
[10] Rhoades, B. E., Fixed point theorems using infinite matrices, Trans. Amer. Math. Soc., 196, 161-176 (1974) · Zbl 0285.47038
[11] Rhoades, B. E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226, 257-290 (1977) · Zbl 0365.54023
[12] Rhoades, B. E., Extensions of some fixed point theorems of Ciric, Maiti and Pal, (Math. Sem. Notes Kobe Univ., 6 (1978)), 41-46 · Zbl 0392.47032
[13] Rhoades, B. E., Comments on two fixed point iteration methods, J. Math. Anal. Appl., 56, 741-750 (1976) · Zbl 0353.47029
[14] Singh, K. L., Fixed point iteration using infinite matrices, (Lakshmikantham, V., Applied Nonlinear Analysis (1979), Academic Press: Academic Press New York), 689-703 · Zbl 0469.47046
[15] Singh, K. L., Generalized contractions and the sequence of iterates, (Lakshmikantham, V., Nonlinear Equations in Abstract Spaces (1978), Academic Press: Academic Press New York), 439-462 · Zbl 0469.47045
[16] Tricomi, F., Un teorema sulla convergenza della successioni formate dalle successive iterate di una funzione di una variable reale, Giorn. Mat. Battaglini, 54, 1-19 (1916)
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