
02361810
j
2004f.04869
A generalization of Brian Fisher's theorem.
Math. Educ. 38, No. 2, 9294 (2004).
2004
Kumar Pankaj, Siwan, Bihar, India; I.M. Prasad, Siwan, Bihar, India
EN
I95
self maps
associated sequences
metric spaces
common fixed points
Suppose $S$ and $T$ are selfmaps of a complete metric space $(X, d)$ satisfying the inequality:$d(Sx, TSy)\le{}c. max \{{}d(x, Sx), d(x, Sy), d(Sy, TSy), ((x, TSy)+d(Sx, Sy))/2\}${} for all $x, y\in{}X$, where $0\le{}c<1$. 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. (Author's abstract)