In classical real analysis, the simplest functions are linear . In convex analysis, the next simplest convex functions (apart from the affine functions, widely used in §B.1.2), are so-called sublinear . We give three motivations for their study.doi:10.1007/978-3-642-56468-0_4Jean-Baptiste...
There exist 0⩽q<1<p and nonnegative functions ã, b̃ on Ω̃ such that≔f(x,s)⩾ã(x)sq+b̃(x)spfora.ex∈Ω̃andalls⩾0,m̃≔(ã)p−1p−q(b̃)1−qp−q≢0onΩ̃,m̃∈Lr(Ω̃)forsomer>N2. Theorem 2.6 Suppose (H6), (H7), (H8)...
Sublinearity and Support Functionsdoi:10.1007/978-3-662-02796-7_5Basic definitions, properties and operations of convex sets (Chap. III) and convex functions (Chap. IV).Jean-Baptiste Hiriart-UrrutyUniversité Paul SabatierClaude LemaréchalINRIA...