Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1216.54009
Aage, C.T.; Salunke, J.N.
The results on fixed points in dislocated and dislocated quasi-metric space.
(English)
[J] Appl. Math. Sci., Ruse 2, No. 57-60, 2941-2948 (2008). ISSN 1312-885X; ISSN 1314-7552/e

Let $X$ be a nonempty set and let $d: X\times X\to [0,\infty)$ be a function satisfying (i) $d(x,y)= d(y,x)= 0\Rightarrow x= y$, (ii) $d(x,y)\le d(x,z)+ d(z,y)$ for all $x,y,z$ in $X$. Then $d$ is called a dislocated quasi-metric for $X$. The couple $(X,d)$ is known as a dislocated quasi-metric space. A typical result in this paper is given below.\par Theorem. Let $(X,d)$ be a complete dislocated quasi-metric space. If $T: X\to X$ is a continuous mapping satisfying $$d(Tx, Ty)\le \alpha\{d(x,Tx)+ d(y,Ty)\},$$ $\forall x,y\in X$ and $0\le\alpha<{1\over 2}$, then $T$ has a unique fixed point.\par Other results include\par Theorem. Let $(X,d)$ be a complete dislocated quasi-metric space. Let $T: X\to X$ be a continuous generalized contraction. Then $T$ has a unique fixed point.\par Theorem. Let $(X,d)$ be a complete dislocated metric space. Let $f,g: X\to X$ be continuous mappings satisfying $$d(fx,gy)\le h\max\{d(x,y), d(x,fx), d(y,gy)\}$$ for all $x,y\in X$. Then $f$ and $g$ have a unique common fixed point.
[K. Chandrasekhara Rao (Kumbakonam)]
MSC 2000:
*54H25 Fixed-point theorems in topological spaces

Keywords: dislocated quasi-metric; fixed point

Cited in: Zbl 1247.54059

Highlights
Master Server