Generalized convex functions and best 𝐿_{𝑝} approximation

Abstract

Some properties of generalized convex functions significant to approximation theory are obtained. The existence of a best L p {L_p} approximation ( 1 ≤ p ≤ ∞ ) (1 \leq p \leq \infty ) from subsets of these functions is established under certain conditions. Special cases of these functions include n n -convex functions which are much investigated in the literature.