A Common End Point Theorem for Set-Valued Generalized <inline-formula> <graphic file="1687-1812-2010-509658-i1.gif"/></inline-formula>-Weak Contraction

We introduce the class of generalized -weak contractive set-valued mappings on a metric space. We establish that such mappings have a unique common end point under certain weak conditions. The theorem obtained generalizes several recent results on single-valued as well as certain set-valued mappings.