Criteria for complex strongly extreme points of Musielak-Orlicz function spaces

The concepts of complex strongly extreme point and complex midpoint local uniform rotundity in complex Banach spaces are introduced. It is proved that every complex strongly extreme point is a complex extreme point and every complex locally uniformly rotund point is a complex strongly extreme point. Moreover, criteria for complex strongly extreme points of the unit ball and, as a corollary, criteria for complex midpoint local uniform rotundity in Musielak-Orlicz function spaces are given.