zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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 approximation of Lipschitz strictly pseudocontractive mappings in uniformly smooth Banach spaces. (English) Zbl 0827.47041
The authors show that certain iterations introduced by {\it S. Ishikawa} [Proc. Am. Math. Soc. 44, 147-150 (1974; Zbl 0286.47036)] involving a so- called pseudo-contractive mapping $T$ in the sense of {\it F. Browder} and {\it W. V. Petryshyn} [J. Math. Anal. Appl. 20, 197-228 (1967; Zbl 0153.457)] converges strongly to a fixed point of $T$. This generalizes a recent result of {\it C. E. Chidume} [Proc. Am. Math. Soc. 99, 283-288 (1987; Zbl 0646.47037)].

MSC:
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47J25Iterative procedures (nonlinear operator equations)
47J05Equations involving nonlinear operators (general)
WorldCat.org
Full Text: DOI
References:
[1] Browder, F. E.; Petryshyn, W. V.: Construction of fixed points of nonlinear mappings in Hilbert space. J. math. Analysis applic. 20, 197-228 (1967) · Zbl 0153.45701
[2] Bogin, J.: On strict pseudo-contractions and a fixed point theorem. Technion preprint series no. MT-219 (1974)
[3] Chidume, C. E.: Iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mappings. Proc. am. Math. soc. 99, 283-288 (1987) · Zbl 0646.47037
[4] Chidume, C. E.: An iterative process for nonlinear Lipschitzian strongly accretive mappings in lp spaces. J. math. Analysis applic. 151, 453-461 (1990) · Zbl 0724.65058
[5] Deng, Lei: An iterative process for nonlinear Lipschitzian strongly accretive mappings in unformly convex and uniformly smooth Banach spaces. Acta appl. Math. 32, 183-196 (1993) · Zbl 0801.47040
[6] Deng, Lei: Iteration processes for nonlinear Lipschitzian strongly accretive mappings in lp spaces. J. math. Analysis applic. 188, 128-140 (1994) · Zbl 0828.47042
[7] Deng, Lei: On chidume’s open questions. J. math. Analysis applic. 174, 741-749 (1993)
[8] Kirk, W. A.: A fixed point theorem for local pseudo-construction in uniformly convex spaces. Manuscripta math. 30, 89-102 (1979) · Zbl 0422.47032
[9] Kirk, W. A.: Remarks on pseudo-construction mappings. Proc. am. Math. soc. 25, 820-823 (1970) · Zbl 0203.14603
[10] Ishikawa, S.: Fixed points by a new iteration method. Proc. am. Math. soc. 44, 147-150 (1974) · Zbl 0286.47036
[11] Istratescu, V. I.: Fixed point theory. (1981) · Zbl 0465.47035
[12] Xu, Zong-Ben; Roach, G. F.: Characteristic inequalities uniformly convex and uniformly smooth Banach spaces. J. math. Analysis applic. 157, 189-210 (1991) · Zbl 0757.46034
[13] Browder, F. E.: Nonlinear mappings of nonexpansive and accretive type in Banach spaces. Bull. am. Math. soc. 73, 875-882 (1967) · Zbl 0176.45302
[14] Kato, T.: Nonlinear semigroups and evolution equations. J. math. Soc. Japan 19, 508-520 (1967) · Zbl 0163.38303
[15] Browder, F. E.: Nonlinear accretive operators in Banach spaces. Bull. am. Math. soc. 73, 470-476 (1967) · Zbl 0159.19905
[16] Browder, F. E.: Nonlinear operators and nonlinear equations of evolution in Banach spaces. Proc. symp. Pure math. 18 (1976) · Zbl 0327.47022
[17] Gwinner, J.: On the convergence of some iteration processes in uniformly convex Banach spaces. Proc. am. Math. soc. 71, 29-35 (1978) · Zbl 0393.47040
[18] Morales, C.: Pseudocontractive mappings and Leray Schauder boundary condition. Commentat. math. Univ. carol. 20, 745-756 (1979) · Zbl 0429.47021
[19] Nevalinna, O.; Reich, S.: Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces. Israel J. Math. 32, 44-58 (1979) · Zbl 0427.47049
[20] Petryshyn, W. V.: Construction of fixed points of demi-compact mappings in Hilbert space. J. math. Analysis applic. 14, 276-284 (1986) · Zbl 0138.39802
[21] Lindenstrauss, J.; Tsafriri, L.: Classical Banach spaces, II. (1979)
[22] Dunn, J. C.: Iterative construction of fixed points for multivalued operators of the monotone type. J. funct. Analysis 27, 38-50 (1978) · Zbl 0422.47033
[23] Deimling, K.: Zeros of accretive operators. Manuscripta math. 13, 365-375 (1974) · Zbl 0288.47047