Point spectrum and existence results for a pair of duality mappings corresponding to different gauge functions

Abstract

Some existence results for a couple of duality mappings corresponding to different gauge functions are obtained in connection with their numerical range and point spectrum. The techniques used come from the theory of monotone operators (in particular, the Browder's surjectivity theorem) and from that of the Leray-Schauder topological degree (in particular, the
Leray-Schauder-Schaefer theorem).