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Iterative solution of nonlinear equations involving strongly accretive operators without the Lipschitz assumption. (English) Zbl 0896.47048
Let $E$ be a real Banach space with a uniformly convex dual space $E^*$. Suppose $T: E\to E$ is a continuous (not necessarily Lipschitzian) strongly accretive map such that $(I- T)$ has bounded range, where $I$ denotes the identity operator. It is proved that the Ishikawa iterative sequence converges strongly to the unique solution of the equation $Tx= f$, $f\in E$.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H06Accretive operators, dissipative operators, etc. (nonlinear)
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References:
[1] Browder, F. E.: Nonlinear mappings of nonexpansive and accretive type in Banach spaces. Bull. amer. Math. soc. 73, 875-882 (1967) · Zbl 0176.45302
[2] Browder, F. E.: Nonlinear operators and nonlinear equations of evolution in Banach spaces. Proc. sympos. Pure. math. 18 (1976) · Zbl 0327.47022
[3] Kato, T.: Nonlinear semigroups and evolution equations. J. math. Soc. Japan 18/19, 508-520 (1967) · Zbl 0163.38303
[4] Barbu, V.: Nonlinear semigroups and differential equations in Banach spaces. (1976) · Zbl 0328.47035
[5] Chidume, C. E.: Iterative solution of nonlinear equations with strongly accretive operators. J. math. Anal. appl. 192, 502-518 (1995) · Zbl 0868.47040
[6] Chidume, C. E.: Approximation of fixed points of strongly pseudocontractive mappings. Proc. amer. Math. soc. 120, 545-551 (1994) · Zbl 0802.47058
[7] Chidume, C. E.: An iterative process for nonlinear Lipschitzian strongly accretive mappings inlpspaces. J. math. Anal. appl. 151, 453-461 (1990) · Zbl 0724.65058
[8] Deimling, K.: Zeros of accretive operators. Manuscripta math. 13, 283-288 (1974) · Zbl 0288.47047
[9] Morales, C.: Surjectivity theorems for multi-valued mappings of accretive type. Comment. math. Univ. carolin. 26 (1985) · Zbl 0595.47041
[10] Reich, S.: An iterative procedure for constructing zeros of accretive sets in Banach spaces. Nonlinear anal. 2, 85-92 (1978) · Zbl 0375.47032
[11] Weng, X. L.: Fixed point iteration for local strictly pseudo-contractive mapping. Proc. amer. Math. soc. 113, 727-731 (1991) · Zbl 0734.47042
[12] Tan, K. K.; Xu, H. K.: Iterative solution to nonlinear equations of strongly accretive operators in Banach spaces. J. math. Anal. appl. 178, 9-21 (1993) · Zbl 0834.47048
[13] J. Bogin, 1974, On strict pseudo--contractions and a fixed point theorem
[14] Jr., R. H. Martin: A global existence theorem for autonomous differential equations in Banach spaces. Proc. amer. Math. soc. 26, 307-314 (1970)
[15] Mann, W. R.: Mean value methods in iteration. Proc. amer. Math. soc. 4, 506-510 (1953) · Zbl 0050.11603
[16] Ishikawa, S.: Fixed point and iteration of a nonexpansive mapping in a Banach space. Proc. amer. Math. soc. 73, 65-71 (1976) · Zbl 0352.47024
[17] Gwinner, J.: On the convergence of some iteration processes in uniformly convex Banach spaces. Proc. amer. Math. soc. 81, 29-35 (1978) · Zbl 0393.47040