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)
Multivalued nonexpansive mappings in Banach spaces. (English) Zbl 0988.47034
Using the technique of asymptotic centers a few fixed point theorems are proved for nonexpansive multivalued mappings acting from a nonempty closed bounded convex subset $E$ of a Banach space $X$ into the family of nonempty compact convex subsets of $X$. It is assumed that considered mappings satisfy an extra condition expressed in terms of the so-called inwardness.

47H09Mappings defined by “shrinking” properties
47H04Set-valued operators
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[1] Caristi, Ca.J.: Fixed point theorems for mappings satisfying inwardness conditions. Trans. amer. Math. soc. 215, 241-251 (1976) · Zbl 0305.47029
[2] K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin, 1992. · Zbl 0760.34002
[3] Downing, D.; Kirk, W. A.: Fixed point theorems for set-valued mappings in metric and Banach spaces. Math. japonica 22, 99-112 (1977) · Zbl 0372.47030
[4] Edelstein, M.: The construction of an asymptotic center with a fixed point property. Bull. amer. Math. soc. 78, 206-208 (1972) · Zbl 0231.47029
[5] Goebel, K.: On a fixed point theorem for multivalued nonexpansive mappings. Ann. univ. M. Curie-sklowdska 29, 70-72 (1975) · Zbl 0365.47032
[6] Huff, R. E.: Banach spaces which are nearly uniformly convex. Rocky mountain J. Math. 10, 743-749 (1980) · Zbl 0505.46011
[7] J.L. Kelly, General Topology, van Nostrand, Princeton, NJ, 1955.
[8] W.A. Kirk, Nonexpansive mappings in product spaces, set-valued mappings and k-uniform rotundity, in: F.E. Browder (Ed.), Non-linear Functional Analysis and Applications, Proceedings of the Symposium Pure Mathematics, Vol. 45, Part 2, American Mathematical Society, Providence, RI, 1986, pp. 51--64. · Zbl 0594.47048
[9] Kirk, W. A.; Massa, S.: Remarks on asymptotic and Chebyshev centers. Houston J. Math. 16, 357-364 (1990) · Zbl 0729.47053
[10] Kuczumow, T.; Prus, S.: Compact asymptotic centers and fixed points of multivalued nonexpansive mappings. Houston J. Math. 16, 465-468 (1990) · Zbl 0724.47033
[11] Dozo, E. Lami: Multivalued nonexpansive mappings and Opial’s condition. Proc. amer. Math. soc. 38, 286-292 (1973) · Zbl 0268.47060
[12] Lim, T. C.: A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space. Bull. amer. Math. soc. 80, 1123-1126 (1974) · Zbl 0297.47045
[13] Lim, T. C.: Remarks on some fixed point theorems. Proc. amer. Math. soc. 60, 179-182 (1976) · Zbl 0346.47046
[14] Nadler, S. B.: Multivalued contraction mappings. Pacific J. Math. 30, 475-488 (1969) · Zbl 0187.45002
[15] Opial, Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. amer. Math. soc. 73, 595-597 (1967) · Zbl 0179.19902
[16] Reich, S.: Approximate selections, best approximations, fixed points, and invariant sets. J. math. Anal. appl. 62, 104-113 (1978) · Zbl 0375.47031
[17] Sullivan, F.: A generalization of uniformly rotund Banach spaces. Can. J. Math. 31, 628-636 (1979) · Zbl 0422.46011
[18] Xu, H. K.: Inequalities in Banach spaces with applications. Nonlinear anal. 16, 1127-1138 (1991) · Zbl 0757.46033
[19] E. Zeidler, Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems, Springer, New York, 1986. · Zbl 0583.47050