Complex Convexity of Orlicz Modular Sequence Spaces

Abstract

The concepts of complex extreme points, complex strongly extreme points, complex strict convexity, and complex midpoint locally uniform convexity in general modular spaces are introduced. Then we prove that, for any Orlicz modular sequence spacelΦ,ρ,lΦ,ρis complex midpoint locally uniformly convex. As a corollary,lΦ,ρis also complex strictly convex.