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)
Fixed point theory for set-valued quasi-contraction maps in metric spaces. (English) Zbl 1230.54034
Summary: We give a fixed point theorem for set-valued quasi-contraction maps in metric spaces. Our main result improves some well-known results from the literature.

54H25Fixed-point and coincidence theorems in topological spaces
54C60Set-valued maps (general topology)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
[1]Ćirić, L. B.: A generalization of Banach’s contraction principle, Proc. amer. Math. soc. 45, No. 2, 267-273 (1974) · Zbl 0291.54056 · doi:10.2307/2040075
[2]Nadler, S. B.: Multi-valued contraction mappings, Pacific J. Math. 30, 475-488 (1969) · Zbl 0187.45002
[3]Mizoguchi, N.; Takahashi, W.: Fixed point theorems for multivalued mappings on complete metric spaces, J. math. Anal. appl. 141, 177-188 (1989) · Zbl 0688.54028 · doi:10.1016/0022-247X(89)90214-X
[4]B. Djafari Rouhani, S. Moradi, Common fixed point of multivalued generalized ϕ-weak contractive mappings, Fixed Point Theory and Applications, vol. 2010, Article ID 708984, 13 pages. · Zbl 1202.54041 · doi:10.1155/2010/708984
[5]Daffer, P. Z.; Kaneko, H.: Fixed points of generalized contractive multi-valued mappings, J. math. Anal. appl. 192, 655-666 (1995) · Zbl 0835.54028 · doi:10.1006/jmaa.1995.1194
[6]Rezapour, Sh.; Haghi, R. H.; Shahzad, N.: Some notes on fixed points of quasi-contraction maps, Appl. math. Lett. 23, No. 4, 498-502 (2010) · Zbl 1206.54061 · doi:10.1016/j.aml.2010.01.003
[7]Al-Thagafi, M. A.; Shahzad, N.: Coincidence points, generalized I-nonexpansive multimaps, and applications, Nonlinear anal. 67, 2180-2188 (2007) · Zbl 1125.47038 · doi:10.1016/j.na.2006.08.042
[8]O’regan, D.; Shahzad, N.: Invariant approximations for generalized I-contractions, Numer. funct. Anal. optim. 26, 565-575 (2005) · Zbl 1084.41023 · doi:10.1080/NFA-200067306
[9]O’regan, D.; Shahzad, N.: Coincidence points and invariant approximation results for multimaps, Acta math. Sin. (Engl. Ser.) 23, 1601-1610 (2007) · Zbl 1131.54030 · doi:10.1007/s10114-005-0768-1