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)
Extension of Caristi’s fixed point theorem to vector valued metric spaces. (English) Zbl 1231.54017
Summary: The paper deals with the classical Caristi fixed point theorem in vector valued metric spaces. The results obtained seem to be new in this setting.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
References:
[1]Brønsted, A.: Fixed point and partial orders, Proc. amer. Math. soc. 60, 365-366 (1976)
[2]Caristi, J.: Fixed point theorems for mappings satisfying inwardness conditions, Trans. amer. Math. soc. 215, 241-251 (1976) · Zbl 0305.47029 · doi:10.2307/1999724
[3]Caristi, J.: Fixed point theory and inwardness conditions, Appl. nonlinear anal., 479-483 (1979) · Zbl 0462.47039
[4]Halpern, B.; Bergman, G.: A fixed point theorem for inward and outward maps, Trans. amer. Math. soc. 130, 353-358 (1968) · Zbl 0153.45602 · doi:10.2307/1994976
[5]F.E. Browder, On a theorem of Caristi and Kirk, in: Proc. Seminar on Fixed Point Theory and Its Applications, Dalhousie University, June 1975, Academic Press, pp. 23–27. · Zbl 0379.54016
[6]Kirk, W. A.; Caristi, J.: Mapping theorems in metric and Banach spaces, Bull. l’acad. Polon. sci. 25, 891-894 (1975) · Zbl 0313.47041
[7]Ekeland, I.: Sur LES problemes variationnels, C. R. Acad. sci. Paris 275, 1057-1059 (1972) · Zbl 0249.49004
[8]Sullivan, F.: A characterization of complete metric spaces, Proc. amer. Math. soc. 85, 345-346 (1981) · Zbl 0468.54021 · doi:10.2307/2043524
[9]Agarwal, R. P.: Contraction and approximate contraction with an application to multi-point boundary value problems, J. comput. Appl. math. 9, 315-325 (1983) · Zbl 0546.65060 · doi:10.1016/0377-0427(83)90003-1
[10]Urabe, M.: An existence theorem for multi-point boundary value problems, Funkcial. ekvac. 9, 43-60 (1966) · Zbl 0168.06502
[11]Bernfeld, S. R.; Lakshmikantham, V.: An introduction to nonlinear boundary value problems, (1974)
[12]Suzuki, T.: Generalized caristi’s fixed point theorems by bae and others, J. math. Anal. appl. 302, 502-508 (2005) · Zbl 1059.54031 · doi:10.1016/j.jmaa.2004.08.019
[13]Khamsi, M. A.: Remarks on caristi’s fixed point theorem, Nonlinear anal. 71, 227-231 (2009) · Zbl 1175.54056 · doi:10.1016/j.na.2008.10.042