most recent 30 from http://mathoverflow.net 2013-05-22T13:17:48Z http://mathoverflow.net/feeds/user/18769 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/79072/if-tx-rightarrow-cbx-be-a-weak-contraction-multi-valued-mapping farshid khojasteh 2011-10-25T12:58:37Z 2011-10-25T12:58:37Z

<p>If $T:X \rightarrow CB(X)$ be a weak contraction multi valued mapping by closed values, i.e., </p> <p>$H(Tx,Ty)\leq d(x,y)-\phi(d(x,y))$</p> <p>where $\phi:R^+\rightarrow R^+$ be a mapping satisfies $ \phi(t)&lt; t $ and $ \phi(0)=0$ and $\liminf_{t\rightarrow\infty}(t-\phi(t))> 0$ then, does $T$ have a fixed point?</p>