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)
On fixed points of quasi-contraction type multifunctions. (English) Zbl 1243.54062
Summary: D. Ilić and V. Rakočević [Appl. Math. Lett. 22, No. 5, 728–731 (2009; Zbl 1179.54060)] proved that quasi-contraction maps on normal cone metric spaces have a unique fixed point. Then, Kadelburg, Radenović and Rakočević generalized their results by considering an additional assumption [Z. Kadelburg, S. Radenović and V. Rakočević, Appl. Math. Lett. 22, No. 11, 1674–1679 (2009; Zbl 1180.54056)]. Also, they proved that quasi-contraction maps on cone metric spaces have the property (P) whenever λ(0,1 2). Later, Haghi, Rezapour and Shahzad proved same results without the additional assumption and for λ(0,1) by providing a new technical proof [Sh. Rezapour, R.H. Haghi and N. Shahzad, Appl. Math. Lett. 23, No. 4, 498–502 (2010; Zbl 1206.54061)]. In 2011, D. Wardowski published a paper [Appl. Math. Lett. 24, No. 3, 275–278 (2011; Zbl 1206.54067)] and tried to test fixed point results for multifunctions on normal cone metric spaces. Of course, he used a special view in his results. Recently, Amini-Harandi proved a result on the existence of fixed points of set-valued quasi-contraction maps in metric spaces by using the technique of Rezapour et al. [Zbl 1206.54061]. But, like Kadelburg et al. [Zbl 1180.54056], he could prove it only for λ(0,1 2) A. Amini-Harandi [Appl. Math. Lett. 24, No. 11, 1791–1794 (2011; Zbl 1230.54034)]. In this work, we prove again the main result of Amini-Harandi [Zbl 1230.54034] by using a simple method. Also, we introduce quasi-contraction type multifunctions and show that the main result of Amini-Harandi [Zbl 1230.54034] holds for quasi-contraction type multifunctions.
54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces
54C60Set-valued maps (general topology)
[1]Ćirić, Lj.: Fixed point theory: contraction mapping principle, (2003)
[2]Pathak, H. K.; Shahzad, N.: Fixed point results for generalized quasicontraction mappings in abstract metric spaces, Nonlinear anal. 71, 6068-6076 (2009) · Zbl 1189.54036 · doi:10.1016/j.na.2009.05.052
[3]Amini-Harandi, A.: Fixed point theory for set-valued quasi-contraction maps in metric spaces, Appl. math. Lett. 24, 1791-1794 (2011) · Zbl 1230.54034 · doi:10.1016/j.aml.2011.04.033
[4]Rezapour, Sh.; Haghi, R. H.; Shahzad, N.: Some notes on fixed points of quasi-contraction maps, Appl. math. Lett. 23, 498-502 (2010) · Zbl 1206.54061 · doi:10.1016/j.aml.2010.01.003
[5]Haghi, R. H.; Rezapour, Sh.; Shahzad, N.: Some fixed point generalizations are not real generalizations, Nonlinear anal. 74, 1799-1803 (2011)
[6]Ilić, D.; Rakocević, V.: Quasi-contraction on a cone metric space, Appl. math. Lett. 22, 728-731 (2009) · Zbl 1179.54060 · doi:10.1016/j.aml.2008.08.011
[7]Kadelburg, Z.; Radenović, S.; Rakocević, V.: Remarks on ”quasi-contraction on a cone metric space”, Appl. math. Lett. 22, 1674-1679 (2009) · Zbl 1180.54056 · doi:10.1016/j.aml.2009.06.003
[8]Wardowski, D.: On set-valued contractions of nadler type in cone metric spaces, Appl. math. Lett. 24, 275-278 (2011) · Zbl 1206.54067 · doi:10.1016/j.aml.2010.10.003