This study focuses on extending the established theory of nonexpansive mappings. Specifically, we introduce and formally define the class of Kannan type mappings relative to orbits within the setting of a general Banach space. Following this definition, we establish a fundamental characterization: we prove that a Banach space A is endowed with weak normal structure if and only if it guarantees the existence of a weakly fixed point for every mapping belonging to this newly introduced class of Kannan type mappings with respect to orbits
