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If $T:X \rightarrow CB(X)$ be a weak contraction multi valued mapping by closed values, i.e.,

$H(Tx,Ty)\leq d(x,y)-\phi(d(x,y))$

where $\phi:R^+\rightarrow R^+$ be a mapping satisfies $ \phi(t)< t $ and $ \phi(0)=0$ and $\liminf_{t\rightarrow\infty}(t-\phi(t))> 0$ then, does $T$ have a fixed point?

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What is the map $H$? – Christopher A. Wong Oct 25 2011 at 22:49

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