Advanced Search

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]