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Zbl 0591.54037
Popa, Valeriu
Common fixed points for multifunctions satisfying a rational inequality. (English)
[J] Kobe J. Math. 2, 23-28 (1985). ISSN 0289-9051

The author proves a common fixed point theorem for two multifunctions $T\sb 1$ and $T\sb 2$ defined on a complete metric space. The mappings satisfy a very technical rational inequality of generalized contractive type which in the case $T=T\sb 1=T\sb 2$ is single-valued reduces to $$ d\sp m(Tx,Ty)\le c\cdot \frac{d\sp p(x,Tx)+d\sp p(y,Ty)}{d\sp{p- m}(x,Tx)+d\sp{p-m\quad}(y,Ty)}. $$ $c<1$, $p\ge 2$, $m<p$. Related results are obtained for sequences.
[W.A.Kirk]

MSC 2000:: *54H25 Fixed-point theorems in topological spaces
54C60 Set-valued maps

Keywords: generalized contraction; common fixed point; complete metric space

Cited in: Zbl 0802.54029

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