Abstract
Suppose X=L p (orl p),p>2, T:D(T)→X is a locally Lipschitzian and strictly accretive operator. In this paper, the iterative approximation of the solution of nonlinear equation Tx=y is given and the iterative approximation of a fixed point of a locally Lipschitzian and strictly pseudo-contractive mapping is discussed.
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References
Browder, F. E., Nonlinear mapping of nonexpansive and accretive type in Banach space,Bull. Amer. Math. Soc.,73 (1967), 875–882.
Bynum, W. L., Weak parallelogram laws for Banach spaces,Canad. Math. Bull. 19 (1976). 269–275.
Chidume, C. E., Iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mapping,Pro. Amer. Math. Soc.,99, 2 (1987), 283–288.
Kato, T., Nonlinear semigroups and evolution equation,J. Math. Soc. Japan,19 (1967), 508–520.
Morales, C., Pseudo-contractive mappings and Leray Schauder boundary conditions,Comment. Math. Univ. Carolina,20, 4 (1979), 745–756.
Patter, W. M., Iterative methods for the solution of a linear operator equation in Hilbert space, A survey,Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, New-York (1974).
Rhoades, B. E., Fixed point interation using infinite matrices,Tran. Amer. Math. Soc.,196 (1974), 161–178.
Rockafellar, R. T., Local boundness of nonlinear monotone operator,Michigan Math. J.,16 (1969), 397–407.
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Communicated by Xu Ci-da and Wu Jia-long
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Bao-kang, Z. Iterative approximation of the solution of a locally Lipschitzian equation. Appl Math Mech 12, 409–414 (1991). https://doi.org/10.1007/BF02020404
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DOI: https://doi.org/10.1007/BF02020404