id: 02361810
dt: j
an: 2004f.04869
au:
ti: A generalization of Brian Fisherâ€™s theorem.
so: Math. Educ. 38, No. 2, 92-94 (2004).
py: 2004
pu: Kumar Pankaj, Siwan, Bihar, India; I.M. Prasad, Siwan, Bihar, India
la: EN
cc: I95
ut: self maps; associated sequences; metric spaces; common fixed points
ci:
li:
ab: Suppose $S$ and $T$ are self-maps of a complete metric space $(X, d)$
satisfying the inequality:$d(Sx, TSy)\lec. max \{d(x, Sx), d(x, Sy),
d(Sy, TSy), ((x, TSy)+d(Sx, Sy))/2\}$ for all $x, y\inX$, where
$0\lec<1$. Brian Fisher has proved that if either $S$ or $T$ is
continuous then $S$ and $T$ have a unique common fixed point. In this
paper, we obtain a generalization of this result by relaxing the
completeness of $X$ and dropping the condition of continuity.
(Authorâ€™s abstract)
rv: