weak fixed point property for kannan type mappings with respect to orbits in banach spaces

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.