Metric generalized inverse of multi-valued linear operator in arbitrary Banach spaces

The metric generalized inverse of multi-valued linear operator in arbitrary Banach spaces is inverstigated, characterizations of least extremal solutions in terms of metric operator parts and metric generalized inverses of multi-valued linear operator are given by the methods of geometry of Banach spaces. These results indeed extend and improve the corresponding works done by Y. W. Wang, J. Liu (2005) and others from reflexive strictly convex Banach space to the general Banach space.