zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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 $Tx= f$, $f\in E$.

47J25Iterative procedures (nonlinear operator equations)
47H06Accretive operators, dissipative operators, etc. (nonlinear)
Full Text: DOI
[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