# 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)
Common fixed point results for noncommuting mappings without continuity in cone metric spaces. (English) Zbl 1147.54022

Let $\left(X,d\right)$ be a cone metric space and $P$ a normal cone with a constant. Let maps $f,g:X\to X$ be such that $f\left(X\right)\subseteq g\left(X\right),g\left(X\right)$ is a complete subspace of $X$ and $f,g$ are commuting at their coincidence points. Further let for any $x,y$ in $X$,

$d\left(fx,fy\right)\le ad\left(gx,gy\right)+b\left[d\left(fx,gx\right)+d\left(fy,gy\right)\right]+c\left[d\left(fx,gy\right)+d\left(fy,gx\right)\right],$

where $a\ge 0,b\ge 0,c\ge 0$ and $a+2b+2c<1·$ Then the authors, extending a result of G. Jungck [Am. Math. Mon. 83, 261–263 (1976; Zbl 0321.54025)] (respectively, R. Kannan [Bull. Calcutta Math. Soc. 60, 71–76 (1968; Zbl 0209.27104)]), show in Theorem 2.1 with $a=k,b=c=0$ (respectively, in Theorem 2.3, with $a=c=0,b=k$) that $f$ and $g$ have a unique common fixed point. They obtain the same conclusion in Theorem 2.4 with $a=b=0,c=k$. (In Theorem 2.4, “$d\left(fx,fy\right)\le$” is misprinted as ”$d\left(fx,fy\right)<$”.)

##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces 47H10 Fixed point theorems for nonlinear operators on topological linear spaces