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)
$\varphi$-pairs and common fixed points in cone metric spaces. (English) Zbl 1164.54031
Summary: In this paper, we introduce a contractive condition, called $\varphi$-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which assures existence and uniqueness of common fixed points for $\varphi$-pairs. We also obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature.

54H25Fixed-point and coincidence theorems in topological spaces
54F05Linearly, generalized, and partial ordered topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[1] Abbas, M., Jungck, G.: Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416--420 · Zbl 1147.54022 · doi:10.1016/j.jmaa.2007.09.070
[2] Huang, L.-G., Zhang, X.: Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468--1476 · Zbl 1118.54022 · doi:10.1016/j.jmaa.2005.03.087
[3] Jungck, G.: Commuting maps and fixed points, Amer. Math. Monthly, 83 (1976), 261--263 · Zbl 0321.54025 · doi:10.2307/2318216
[4] Jungck, G.: Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771--779 · Zbl 0613.54029 · doi:10.1155/S0161171286000935
[5] Jungck, G.: Common fixed points for noncontinuous nonself maps on non-metric spaces, Far East J. Math. Sci. (FJMS), 4 (1996), 199--215 · Zbl 0928.54043
[6] Jungck, G., Rhoades, B.E: Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227--238 · Zbl 0904.54034
[7] Pant, R.P.: Common fixed points of noncommuting mappings, J. Math. Anal. Appl., 188 (1994), 436--440 · Zbl 0830.54031 · doi:10.1006/jmaa.1994.1437
[8] Rezapour, Sh., Hamlbarani, R.: Some notes on the paper ”Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345 (2008), 719--724 · Zbl 1145.54045 · doi:10.1016/j.jmaa.2008.04.049
[9] Sessa, S.: On a weak commutativity condition of mappings in fixed point consideration, Publ. Inst. Math. Soc., 32 (1982), 149--153 · Zbl 0523.54030
[10] Vetro, P.: Common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 56 (2007), 464--468 · Zbl 1196.54086 · doi:10.1007/BF03032097