Generalized convex functions and best 𝐿_{𝑝} approximation

Mathsen, Ronald M.; Ubhaya, Vasant A.

doi:10.1090/S0002-9939-1992-1088444-4

Generalized convex functions and best $L_ p$ approximation
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by Ronald M. Mathsen and Vasant A. Ubhaya PDF

Proc. Amer. Math. Soc. 114 (1992), 733-740 Request permission

Abstract:

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

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Best

-approximation by generalized convex functions

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