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 theorems for Reich type contractions on metric spaces with a graph. (English) Zbl 1250.54044
The paper presents a fixed point theorem for so-called Reich type operators in metric spaces endowed with a connected graph. The result generalize some recent results of this type given by J. Jachymski in [“The contraction principle for mappings on a metric space with a graph”, Proc. Am. Math. Soc. 136, No. 4, 1359–1373 (2008; Zbl 1139.47040)].
54H25Fixed-point and coincidence theorems in topological spaces
54E40Special maps on metric spaces
54E50Complete metric spaces
[1]Petruşel, A.; Rus, I. A.: Fixed point theorems in ordered L-spaces, Proc. amer. Math. soc. 134, 411-418 (2006) · Zbl 1086.47026 · doi:10.1090/S0002-9939-05-07982-7
[2]Johnsonbaugh, R.: Discrete math., (1997)
[3]Jachymski, J.: The contraction principle for mappings on a metric space with a graph, Proc. amer. Math. soc. 1, No. 136, 1359-1373 (2008) · Zbl 1139.47040 · doi:10.1090/S0002-9939-07-09110-1
[4]Bega, I.; Butt, A. R.; Radojević, S.: The contraction principle for set valued mappings on a metric space with a graph, Comput. math. Appl. 60, 1214-1219 (2010) · Zbl 1201.54029 · doi:10.1016/j.camwa.2010.06.003
[5]Bojor, F.: Fixed point of φ-contraction in metric spaces endowed with a graph, Ann. univ. Craiova math. Comput. sci. Ser. 37, No. 4, 85-92 (2010) · Zbl 1215.54018
[6]Reich, S.: Fixed points of contractive functions, Boll. unione mat. Ital. 5, 26-42 (1972) · Zbl 0249.54026
[7]Ćirić, L. B.: A generalization of Banach’s contraction principle, Proc. amer. Math. soc. 45, 267-273 (1974) · Zbl 0291.54056 · doi:10.2307/2040075
[8]Rus, I. A.; Petruşel, A.; Petruşel, G.: Fixed point theory, (2008)
[9]Petric, M. A.: Some remarks concerning ciric-reich-rus operators, Creat. math. Inform. 18, No. 2, 188-193 (2009)